Exemple #1
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    def from_conf(conf, options):
        from sfepy.discrete import FieldVariable, Variables, Problem
        from sfepy.discrete.fem import Mesh, FEDomain, Field

        mesh = Mesh.from_file(data_dir + '/meshes/2d/square_unit_tri.mesh')
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')
        domain.create_region('Left', 'vertices in (x < -0.499)', 'facet')
        domain.create_region(
            'LeftStrip', 'vertices in (x < -0.499)'
            ' & (y > -0.199) & (y < 0.199)', 'facet')
        domain.create_region('LeftFix', 'r.Left -v r.LeftStrip', 'facet')
        domain.create_region('Right', 'vertices in (x > 0.499)', 'facet')
        domain.create_region(
            'RightStrip', 'vertices in (x > 0.499)'
            ' & (y > -0.199) & (y < 0.199)', 'facet')
        domain.create_region('RightFix', 'r.Right -v r.RightStrip', 'facet')

        fu = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
        u = FieldVariable('u', 'unknown', fu)

        fp = Field.from_args('fp', nm.float64, 'scalar', omega, approx_order=2)
        p = FieldVariable('p', 'unknown', fp)

        pb = Problem('test', domain=domain, fields=[fu, fp], auto_conf=False)

        test = Test(problem=pb,
                    variables=Variables([u, p]),
                    conf=conf,
                    options=options)
        return test
Exemple #2
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    def test_interpolation_two_meshes(self):
        from sfepy import data_dir
        from sfepy.discrete import Variables
        from sfepy.discrete.fem import Mesh, FEDomain, Field

        m1 = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')

        m2 = Mesh.from_file(data_dir + '/meshes/3d/cube_medium_tetra.mesh')
        m2.coors[:] *= 2.0

        bbox = m1.get_bounding_box()
        dd = bbox[1, :] - bbox[0, :]
        data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])

        variables1 = {
            'u': ('unknown field', 'scalar_tp', 0),
            'v': ('test field', 'scalar_tp', 'u'),
        }

        variables2 = {
            'u': ('unknown field', 'scalar_si', 0),
            'v': ('test field', 'scalar_si', 'u'),
        }

        d1 = FEDomain('d1', m1)
        omega1 = d1.create_region('Omega', 'all')
        field1 = Field.from_args('scalar_tp',
                                 nm.float64, (1, 1),
                                 omega1,
                                 approx_order=1)
        ff1 = {field1.name: field1}

        d2 = FEDomain('d2', m2)
        omega2 = d2.create_region('Omega', 'all')
        field2 = Field.from_args('scalar_si',
                                 nm.float64, (1, 1),
                                 omega2,
                                 approx_order=0)
        ff2 = {field2.name: field2}

        vv1 = Variables.from_conf(transform_variables(variables1), ff1)
        u1 = vv1['u']
        u1.set_from_mesh_vertices(data)

        vv2 = Variables.from_conf(transform_variables(variables2), ff2)
        u2 = vv2['u']

        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)

        fname = in_dir(self.options.out_dir)
        u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
        u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))

        return True
Exemple #3
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    def test_projection_iga_fem(self):
        from sfepy.discrete import FieldVariable
        from sfepy.discrete.fem import FEDomain, Field
        from sfepy.discrete.iga.domain import IGDomain
        from sfepy.mesh.mesh_generators import gen_block_mesh
        from sfepy.discrete.iga.domain_generators import gen_patch_block_domain
        from sfepy.discrete.projections import (make_l2_projection,
                                                make_l2_projection_data)

        shape = [10, 12, 12]
        dims = [5, 6, 6]
        centre = [0, 0, 0]
        degrees = [2, 2, 2]

        nurbs, bmesh, regions = gen_patch_block_domain(dims, shape, centre,
                                                       degrees,
                                                       cp_mode='greville',
                                                       name='iga')
        ig_domain = IGDomain('iga', nurbs, bmesh, regions=regions)

        ig_omega = ig_domain.create_region('Omega', 'all')
        ig_field = Field.from_args('iga', nm.float64, 1, ig_omega,
                                   approx_order='iga', poly_space_base='iga')
        ig_u = FieldVariable('ig_u', 'parameter', ig_field,
                             primary_var_name='(set-to-None)')

        mesh = gen_block_mesh(dims, shape, centre, name='fem')
        fe_domain = FEDomain('fem', mesh)

        fe_omega = fe_domain.create_region('Omega', 'all')
        fe_field = Field.from_args('fem', nm.float64, 1, fe_omega,
                                   approx_order=2)
        fe_u = FieldVariable('fe_u', 'parameter', fe_field,
                             primary_var_name='(set-to-None)')

        def _eval_data(ts, coors, mode, **kwargs):
            return nm.prod(coors**2, axis=1)[:, None, None]

        make_l2_projection_data(ig_u, _eval_data)

        make_l2_projection(fe_u, ig_u) # This calls ig_u.evaluate_at().

        coors = 0.5 * nm.random.rand(20, 3) * dims

        ig_vals = ig_u.evaluate_at(coors)
        fe_vals = fe_u.evaluate_at(coors)

        ok = nm.allclose(ig_vals, fe_vals, rtol=0.0, atol=1e-12)
        if not ok:
            self.report('iga-fem projection failed!')
            self.report('coors:')
            self.report(coors)
            self.report('iga fem diff:')
            self.report(nm.c_[ig_vals, fe_vals, nm.abs(ig_vals - fe_vals)])

        return ok
Exemple #4
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    def test_projection_iga_fem(self):
        from sfepy.discrete import FieldVariable
        from sfepy.discrete.fem import FEDomain, Field
        from sfepy.discrete.iga.domain import IGDomain
        from sfepy.mesh.mesh_generators import gen_block_mesh
        from sfepy.discrete.iga.domain_generators import gen_patch_block_domain
        from sfepy.discrete.projections import (make_l2_projection,
                                                make_l2_projection_data)

        shape = [10, 12, 12]
        dims = [5, 6, 6]
        centre = [0, 0, 0]
        degrees = [2, 2, 2]

        nurbs, bmesh, regions = gen_patch_block_domain(dims, shape, centre,
                                                       degrees,
                                                       cp_mode='greville',
                                                       name='iga')
        ig_domain = IGDomain('iga', nurbs, bmesh, regions=regions)

        ig_omega = ig_domain.create_region('Omega', 'all')
        ig_field = Field.from_args('iga', nm.float64, 1, ig_omega,
                                   approx_order='iga', poly_space_base='iga')
        ig_u = FieldVariable('ig_u', 'parameter', ig_field,
                             primary_var_name='(set-to-None)')

        mesh = gen_block_mesh(dims, shape, centre, name='fem')
        fe_domain = FEDomain('fem', mesh)

        fe_omega = fe_domain.create_region('Omega', 'all')
        fe_field = Field.from_args('fem', nm.float64, 1, fe_omega,
                                   approx_order=2)
        fe_u = FieldVariable('fe_u', 'parameter', fe_field,
                             primary_var_name='(set-to-None)')

        def _eval_data(ts, coors, mode, **kwargs):
            return nm.prod(coors**2, axis=1)[:, None, None]

        make_l2_projection_data(ig_u, _eval_data)

        make_l2_projection(fe_u, ig_u) # This calls ig_u.evaluate_at().

        coors = 0.5 * nm.random.rand(20, 3) * dims

        ig_vals = ig_u.evaluate_at(coors)
        fe_vals = fe_u.evaluate_at(coors)

        ok = nm.allclose(ig_vals, fe_vals, rtol=0.0, atol=1e-12)
        if not ok:
            self.report('iga-fem projection failed!')
            self.report('coors:')
            self.report(coors)
            self.report('iga fem diff:')
            self.report(nm.c_[ig_vals, fe_vals, nm.abs(ig_vals - fe_vals)])

        return ok
Exemple #5
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def do_interpolation(m2, m1, data, field_name, force=False):
    """Interpolate data from m1 to m2. """
    from sfepy.discrete import Variables
    from sfepy.discrete.fem import FEDomain, Field

    fields = {
        'scalar_si': ((1, 1), 'Omega', 2),
        'vector_si': ((3, 1), 'Omega', 2),
        'scalar_tp': ((1, 1), 'Omega', 1),
        'vector_tp': ((3, 1), 'Omega', 1),
    }

    d1 = FEDomain('d1', m1)

    omega1 = d1.create_region('Omega', 'all')

    f = fields[field_name]

    field1 = Field.from_args('f',
                             nm.float64,
                             f[0],
                             d1.regions[f[1]],
                             approx_order=f[2])
    ff = {field1.name: field1}

    vv = Variables.from_conf(transform_variables(variables), ff)
    u1 = vv['u']
    u1.set_from_mesh_vertices(data)

    d2 = FEDomain('d2', m2)
    omega2 = d2.create_region('Omega', 'all')

    field2 = Field.from_args('f',
                             nm.float64,
                             f[0],
                             d2.regions[f[1]],
                             approx_order=f[2])
    ff2 = {field2.name: field2}

    vv2 = Variables.from_conf(transform_variables(variables), ff2)
    u2 = vv2['u']

    if not force:
        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)

    else:
        coors = u2.field.get_coor()
        vals = u1.evaluate_at(coors, close_limit=0.5)
        u2.set_data(vals)

    return u1, u2
Exemple #6
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    def test_interpolation_two_meshes(self):
        from sfepy import data_dir
        from sfepy.discrete import Variables
        from sfepy.discrete.fem import Mesh, FEDomain, Field

        m1 = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')

        m2 = Mesh.from_file(data_dir + '/meshes/3d/cube_medium_tetra.mesh')
        m2.coors[:] *= 2.0

        bbox = m1.get_bounding_box()
        dd = bbox[1,:] - bbox[0,:]
        data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])

        variables1 = {
            'u'       : ('unknown field', 'scalar_tp', 0),
            'v'       : ('test field',    'scalar_tp', 'u'),
        }

        variables2 = {
            'u'       : ('unknown field', 'scalar_si', 0),
            'v'       : ('test field',    'scalar_si', 'u'),
        }

        d1 = FEDomain('d1', m1)
        omega1 = d1.create_region('Omega', 'all')
        field1 = Field.from_args('scalar_tp', nm.float64, (1,1), omega1,
                                 approx_order=1)
        ff1 = {field1.name : field1}

        d2 = FEDomain('d2', m2)
        omega2 = d2.create_region('Omega', 'all')
        field2 = Field.from_args('scalar_si', nm.float64, (1,1), omega2,
                                 approx_order=0)
        ff2 = {field2.name : field2}

        vv1 = Variables.from_conf(transform_variables(variables1), ff1)
        u1 = vv1['u']
        u1.set_from_mesh_vertices(data)

        vv2 = Variables.from_conf(transform_variables(variables2), ff2)
        u2 = vv2['u']

        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)

        fname = in_dir(self.options.out_dir)
        u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
        u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))

        return True
Exemple #7
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    def from_conf(conf, options):
        import sfepy
        from sfepy.discrete.fem import Mesh, Domain, Field
        mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = Domain('domain', mesh)
        dim = domain.shape.dim

        min_x, max_x = domain.get_mesh_bounding_box()[:,0]
        eps = 1e-8 * (max_x - min_x)

        omega = domain.create_region('Omega', 'all')
        gamma1 = domain.create_region('Gamma1',
                                      'vertices in x < %.10f' % (min_x + eps),
                                      'facet')
        gamma2 = domain.create_region('Gamma2',
                                      'vertices in x > %.10f' % (max_x - eps),
                                      'facet')

        field = Field.from_args('fu', nm.float64, 'vector', omega,
                                approx_order=2)

        test = Test(conf=conf, options=options, dim=dim,
                    omega=omega, gamma1=gamma1, gamma2=gamma2,
                    field=field)
        return test
Exemple #8
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def nodal_stress(out, pb, state, extend=False, integrals=None):
    '''
    Calculate stresses at nodal points.
    '''

    # Point load.
    mat = pb.get_materials()['Load']
    P = 2.0 * mat.get_data('special', 'val')[1]

    # Calculate nodal stress.
    pb.time_update()

    if integrals is None: integrals = pb.get_integrals()

    stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp',
                         integrals=integrals, copy_materials=False)
    sfield = Field.from_args('stress', nm.float64, (3,),
                             pb.domain.regions['Omega'])
    svar = FieldVariable('sigma', 'parameter', sfield,
                         primary_var_name='(set-to-None)')
    svar.set_from_qp(stress, integrals['ivn'])

    print('\n==================================================================')
    print('Given load = %.2f N' % -P)
    print('\nAnalytical solution')
    print('===================')
    print('Horizontal tensile stress = %.5e MPa/mm' % (-2.*P/(nm.pi*150.)))
    print('Vertical compressive stress = %.5e MPa/mm' % (-6.*P/(nm.pi*150.)))
    print('\nFEM solution')
    print('============')
    print('Horizontal tensile stress = %.5e MPa/mm' % (svar()[0]))
    print('Vertical compressive stress = %.5e MPa/mm' % (-svar()[1]))
    print('==================================================================')
    return out
    def from_conf(conf, options):
        import sfepy
        from sfepy.discrete.fem import Mesh, FEDomain, Field
        mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = FEDomain('domain', mesh)
        dim = domain.shape.dim

        min_x, max_x = domain.get_mesh_bounding_box()[:,0]
        eps = 1e-8 * (max_x - min_x)

        omega = domain.create_region('Omega', 'all')
        gamma1 = domain.create_region('Gamma1',
                                      'vertices in x < %.10f' % (min_x + eps),
                                      'facet')
        gamma2 = domain.create_region('Gamma2',
                                      'vertices in x > %.10f' % (max_x - eps),
                                      'facet')

        field = Field.from_args('fu', nm.float64, 'vector', omega,
                                approx_order=2)

        test = Test(conf=conf, options=options, dim=dim,
                    omega=omega, gamma1=gamma1, gamma2=gamma2,
                    field=field)
        return test
Exemple #10
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def _get_bqp(geometry, order):
    from sfepy.discrete import Integral
    from sfepy.discrete.fem.geometry_element import GeometryElement
    from sfepy.discrete.fem import Mesh, FEDomain, Field

    gel = GeometryElement(geometry)

    mesh = Mesh.from_data('aux', gel.coors, None,
                          [gel.conn[None, :]], [[0]], [geometry])
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    surf =  domain.create_region('Surf', 'vertices of surface', 'facet')
    field = Field.from_args('f', nm.float64, shape=1,
                            region=omega, approx_order=1)
    field.setup_surface_data(surf)

    integral = Integral('aux', order=order)
    field.create_bqp('Surf', integral)

    sd = field.surface_data['Surf']
    qp = field.qp_coors[(integral.order, sd.bkey)]

    output('geometry:', geometry, 'order:', order, 'num. points:',
           qp.vals.shape[1], 'true_order:',
           integral.qps[gel.surface_facet_name].order)
    output('min. weight:', qp.weights.min())
    output('max. weight:', qp.weights.max())

    return (gel, qp.vals.reshape((-1, mesh.dim)),
            nm.tile(qp.weights, qp.vals.shape[0]))
Exemple #11
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def prepare_variable(filename, n_components):
    from sfepy.discrete import FieldVariable
    from sfepy.discrete.fem import Mesh, FEDomain, Field

    mesh = Mesh.from_file(filename)

    bbox = mesh.get_bounding_box()
    dd = bbox[1, :] - bbox[0, :]
    data = (nm.sin(4.0 * nm.pi * mesh.coors[:, 0:1] / dd[0]) *
            nm.cos(4.0 * nm.pi * mesh.coors[:, 1:2] / dd[1]))

    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('field',
                            nm.float64,
                            n_components,
                            omega,
                            approx_order=2)

    u = FieldVariable('u',
                      'parameter',
                      field,
                      primary_var_name='(set-to-None)')
    u.set_from_mesh_vertices(data * nm.arange(1, n_components + 1)[None, :])

    return u
Exemple #12
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def nodal_stress(out, pb, state, extend=False, integrals=None):
    """
    Calculate stresses at nodal points.
    """

    # Point load.
    mat = pb.get_materials()["Load"]
    P = 2.0 * mat.get_data("special", "val")[1]

    # Calculate nodal stress.
    pb.time_update()

    if integrals is None:
        integrals = pb.get_integrals()

    stress = pb.evaluate("ev_cauchy_stress.ivn.Omega(Asphalt.D, u)", mode="qp", integrals=integrals)
    sfield = Field.from_args("stress", nm.float64, (3,), pb.domain.regions["Omega"])
    svar = FieldVariable("sigma", "parameter", sfield, primary_var_name="(set-to-None)")
    svar.set_data_from_qp(stress, integrals["ivn"])

    print "\n=================================================================="
    print "Given load = %.2f N" % -P
    print "\nAnalytical solution"
    print "==================="
    print "Horizontal tensile stress = %.5e MPa/mm" % (-2.0 * P / (nm.pi * 150.0))
    print "Vertical compressive stress = %.5e MPa/mm" % (-6.0 * P / (nm.pi * 150.0))
    print "\nFEM solution"
    print "============"
    print "Horizontal tensile stress = %.5e MPa/mm" % (svar()[0][0])
    print "Vertical compressive stress = %.5e MPa/mm" % (-svar()[0][1])
    print "=================================================================="
    return out
def nodal_stress(out, pb, state, extend=False, integrals=None):
    '''
    Calculate stresses at nodal points.
    '''

    # Point load.
    mat = pb.get_materials()['Load']
    P = 2.0 * mat.get_data('special', 'val')[1]

    # Calculate nodal stress.
    pb.time_update()

    if integrals is None: integrals = pb.get_integrals()

    stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp',
                         integrals=integrals, copy_materials=False)
    sfield = Field.from_args('stress', nm.float64, (3,),
                             pb.domain.regions['Omega'])
    svar = FieldVariable('sigma', 'parameter', sfield,
                         primary_var_name='(set-to-None)')
    svar.set_from_qp(stress, integrals['ivn'])

    print('\n==================================================================')
    print('Given load = %.2f N' % -P)
    print('\nAnalytical solution')
    print('===================')
    print('Horizontal tensile stress = %.5e MPa/mm' % (-2.*P/(nm.pi*150.)))
    print('Vertical compressive stress = %.5e MPa/mm' % (-6.*P/(nm.pi*150.)))
    print('\nFEM solution')
    print('============')
    print('Horizontal tensile stress = %.5e MPa/mm' % (svar()[0]))
    print('Vertical compressive stress = %.5e MPa/mm' % (-svar()[1]))
    print('==================================================================') 
    return out
Exemple #14
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def verify_save_dof_maps(field, cell_tasks, dof_maps, id_map, options,
                         verbose=False):
    vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)

    order = options.order
    mesh = field.domain.mesh

    sfield = Field.from_args('aux', nm.float64, 'scalar', field.region,
                             approx_order=order)
    aux = FieldVariable('aux', 'parameter', sfield,
                        primary_var_name='(set-to-None)')
    out = aux.create_output(vec,
                            linearization=Struct(kind='adaptive',
                                                 min_level=order-1,
                                                 max_level=order-1,
                                                 eps=1e-8))

    filename = os.path.join(options.output_dir,
                            'para-domains-dofs.h5')
    if field.is_higher_order():
        out['aux'].mesh.write(filename, out=out)

    else:
        mesh.write(filename, out=out)

    out = Struct(name='cells', mode='cell',
                 data=cell_tasks[:, None, None, None])
    filename = os.path.join(options.output_dir,
                            'para-domains-cells.h5')
    mesh.write(filename, out={'cells' : out})
Exemple #15
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def _get_bqp(geometry, order):
    from sfepy.discrete import Integral
    from sfepy.discrete.fem.geometry_element import GeometryElement
    from sfepy.discrete.fem import Mesh, FEDomain, Field

    gel = GeometryElement(geometry)

    mesh = Mesh.from_data('aux', gel.coors, None, [gel.conn[None, :]], [[0]],
                          [geometry])
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    surf = domain.create_region('Surf', 'vertices of surface', 'facet')
    field = Field.from_args('f',
                            nm.float64,
                            shape=1,
                            region=omega,
                            approx_order=1)
    field.setup_surface_data(surf)

    integral = Integral('aux', order=order)
    field.create_bqp('Surf', integral)

    sd = field.surface_data['Surf']
    qp = field.qp_coors[(integral.order, sd.bkey)]

    output('geometry:', geometry, 'order:', order, 'num. points:',
           qp.vals.shape[1], 'true_order:',
           integral.qps[gel.surface_facet_name].order)
    output('min. weight:', qp.weights.min())
    output('max. weight:', qp.weights.max())

    return (gel, qp.vals.reshape(
        (-1, mesh.dim)), nm.tile(qp.weights, qp.vals.shape[0]))
Exemple #16
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def do_interpolation(m2, m1, data, field_name, force=False):
    """Interpolate data from m1 to m2. """
    from sfepy.discrete import Variables
    from sfepy.discrete.fem import FEDomain, Field

    fields = {
        'scalar_si' : ((1,1), 'Omega', 2),
        'vector_si' : ((3,1), 'Omega', 2),
        'scalar_tp' : ((1,1), 'Omega', 1),
        'vector_tp' : ((3,1), 'Omega', 1),
    }

    d1 = FEDomain('d1', m1)

    omega1 = d1.create_region('Omega', 'all')

    f = fields[field_name]

    field1 = Field.from_args('f', nm.float64, f[0], d1.regions[f[1]],
                             approx_order=f[2])
    ff = {field1.name : field1}

    vv = Variables.from_conf(transform_variables(variables), ff)
    u1 = vv['u']
    u1.set_from_mesh_vertices(data)

    d2 = FEDomain('d2', m2)
    omega2 = d2.create_region('Omega', 'all')

    field2 = Field.from_args('f', nm.float64, f[0], d2.regions[f[1]],
                             approx_order=f[2])
    ff2 = {field2.name : field2}

    vv2 = Variables.from_conf(transform_variables(variables), ff2)
    u2 = vv2['u']

    if not force:
        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)

    else:
        coors = u2.field.get_coor()
        vals = u1.evaluate_at(coors, close_limit=0.5)
        u2.set_data(vals)

    return u1, u2
Exemple #17
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def solveLaplaceEquationTetrahedral(mesh, meshVTK, boundaryPoints,
                                    boundaryConditions):
    """
    mesh: path to a 3D mesh / sfepy mesh
    
    """
    if isinstance(mesh, str):
        mesh = Mesh.from_file(mesh)

    #Set domains
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    boundary = domain.create_region(
        'gamma',
        'vertex  %s' % ','.join(map(str, range(meshVTK.GetNumberOfPoints()))),
        'facet')

    #set fields
    field = Field.from_args('fu', np.float64, 1, omega, approx_order=1)
    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')
    m = Material('m', val=[1.])

    #Define element integrals
    integral = Integral('i', order=3)

    #Equations defining
    t1 = Term.new('dw_laplace( v, u )', integral, omega, v=v, u=u)
    eq = Equation('balance', t1)
    eqs = Equations([eq])

    heatBoundary = boundaryConditions
    points = boundaryPoints

    #Boundary conditions
    c = ClosestPointStupid(points, heatBoundary, meshVTK)

    def u_fun(ts, coors, bc=None, problem=None, c=c):
        c.distances = []
        v = np.zeros(len(coors))
        for i, p in enumerate(coors):
            v[i] = c.interpolate(p)
            #c.findClosestPoint(p)
        return v

    bc_fun = Function('u_fun', u_fun)
    fix1 = EssentialBC('fix_u', boundary, {'u.all': bc_fun})

    #Solve problem
    ls = ScipyDirect({})
    nls = Newton({}, lin_solver=ls)

    pb = Problem('heat', equations=eqs)
    pb.set_bcs(ebcs=Conditions([fix1]))

    pb.set_solver(nls)
    state = pb.solve(verbose=False, save_results=False)
    u = state.get_parts()['u']
    return u
def run(domain, order):
    omega = domain.create_region('Omega', 'all')
    bbox = domain.get_mesh_bounding_box()
    min_x, max_x = bbox[:, 0]
    min_y, max_y = bbox[:, 1]
    eps = 1e-8 * (max_x - min_x)
    gamma1 = domain.create_region('Gamma1',
                                  'vertices in (x < %.10f)' % (min_x + eps),
                                  'facet')
    gamma2 = domain.create_region('Gamma2',
                                  'vertices in (x > %.10f)' % (max_x - eps),
                                  'facet')
    gamma3 = domain.create_region('Gamma3',
                                  'vertices in y < %.10f' % (min_y + eps),
                                  'facet')
    gamma4 = domain.create_region('Gamma4',
                                  'vertices in y > %.10f' % (max_y - eps),
                                  'facet')

    field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)

    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    integral = Integral('i', order=2*order)

    t1 = Term.new('dw_laplace(v, u)',
                  integral, omega, v=v, u=u)
    eq = Equation('eq', t1)
    eqs = Equations([eq])

    fix1 = EssentialBC('fix1', gamma1, {'u.0' : 0.4})
    fix2 = EssentialBC('fix2', gamma2, {'u.0' : 0.0})

    def get_shift(ts, coors, region):
        return nm.ones_like(coors[:, 0])

    dof_map_fun = Function('dof_map_fun', per.match_x_line)
    shift_fun = Function('shift_fun', get_shift)

    sper = LinearCombinationBC('sper', [gamma3, gamma4], {'u.0' : 'u.0'},
                               dof_map_fun, 'shifted_periodic',
                               arguments=(shift_fun,))

    ls = ScipyDirect({})

    pb = Problem('laplace', equations=eqs, auto_solvers=None)

    pb.time_update(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))

    ev = pb.get_evaluator()
    nls = Newton({}, lin_solver=ls,
                 fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)

    pb.set_solver(nls)

    state = pb.solve()

    return pb, state
Exemple #19
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def run(domain, order):
    omega = domain.create_region('Omega', 'all')
    bbox = domain.get_mesh_bounding_box()
    min_x, max_x = bbox[:, 0]
    min_y, max_y = bbox[:, 1]
    eps = 1e-8 * (max_x - min_x)
    gamma1 = domain.create_region('Gamma1',
                                  'vertices in (x < %.10f)' % (min_x + eps),
                                  'facet')
    gamma2 = domain.create_region('Gamma2',
                                  'vertices in (x > %.10f)' % (max_x - eps),
                                  'facet')
    gamma3 = domain.create_region('Gamma3',
                                  'vertices in y < %.10f' % (min_y + eps),
                                  'facet')
    gamma4 = domain.create_region('Gamma4',
                                  'vertices in y > %.10f' % (max_y - eps),
                                  'facet')

    field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)

    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    integral = Integral('i', order=2 * order)

    t1 = Term.new('dw_laplace(v, u)', integral, omega, v=v, u=u)
    eq = Equation('eq', t1)
    eqs = Equations([eq])

    fix1 = EssentialBC('fix1', gamma1, {'u.0': 0.4})
    fix2 = EssentialBC('fix2', gamma2, {'u.0': 0.0})

    def get_shift(ts, coors, region):
        return nm.ones_like(coors[:, 0])

    dof_map_fun = Function('dof_map_fun', per.match_x_line)
    shift_fun = Function('shift_fun', get_shift)

    sper = LinearCombinationBC('sper', [gamma3, gamma4], {'u.0': 'u.0'},
                               dof_map_fun,
                               'shifted_periodic',
                               arguments=(shift_fun, ))

    ls = ScipyDirect({})
    nls = Newton({}, lin_solver=ls)

    pb = Problem('laplace', equations=eqs)

    pb.set_bcs(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))

    pb.set_solver(nls)

    state = pb.solve()

    return pb, state
Exemple #20
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    def test_project_tensors(self):
        from sfepy.discrete import FieldVariable
        from sfepy.discrete.projections import project_by_component

        ok = True

        u = FieldVariable('u',
                          'parameter',
                          self.field,
                          primary_var_name='(set-to-None)')
        u.set_constant(1.0)

        component = FieldVariable('component',
                                  'parameter',
                                  self.field,
                                  primary_var_name='(set-to-None)')

        nls_options = {'eps_a': 1e-16, 'i_max': 1}

        u_qp = u.evaluate()
        u2 = FieldVariable('u2',
                           'parameter',
                           self.field,
                           primary_var_name='(set-to-None)')
        project_by_component(u2,
                             u_qp,
                             component,
                             self.field.approx_order,
                             nls_options=nls_options)

        _ok = self.compare_vectors(u(), u2())
        ok = ok and _ok

        gu_qp = u.evaluate(mode='grad')

        gfield = Field.from_args('gu',
                                 nm.float64,
                                 2,
                                 self.field.region,
                                 approx_order=self.field.approx_order)
        gu = FieldVariable('gu',
                           'parameter',
                           gfield,
                           primary_var_name='(set-to-None)')

        project_by_component(gu,
                             gu_qp,
                             component,
                             gfield.approx_order,
                             nls_options=nls_options)

        _ok = self.compare_vectors(gu(), nm.zeros_like(gu()))
        ok = ok and _ok

        return ok
def solve_problem(shape, dims, young, poisson, force, transform=None):
    domain = make_domain(dims[:2], shape, transform=transform)

    omega = domain.regions['Omega']
    gamma1 = domain.regions['Gamma1']
    gamma2 = domain.regions['Gamma2']

    field = Field.from_args('fu', nm.float64, 6, omega, approx_order=1,
                            poly_space_base='shell10x')
    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    thickness = dims[2]
    if transform is None:
        pload = [[0.0, 0.0, force / shape[1], 0.0, 0.0, 0.0]] * shape[1]

    elif transform == 'bend':
        pload = [[force / shape[1], 0.0, 0.0, 0.0, 0.0, 0.0]] * shape[1]

    elif transform == 'twist':
        pload = [[0.0, force / shape[1], 0.0, 0.0, 0.0, 0.0]] * shape[1]

    m = Material('m', D=sh.create_elastic_tensor(young=young, poisson=poisson),
                 values={'.drill' : 1e-7})
    load = Material('load', values={'.val' : pload})

    aux = Integral('i', order=3)
    qp_coors, qp_weights = aux.get_qp('3_8')
    qp_coors[:, 2] = thickness * (qp_coors[:, 2] - 0.5)
    qp_weights *= thickness

    integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom')

    t1 = Term.new('dw_shell10x(m.D, m.drill, v, u)',
                  integral, omega, m=m, v=v, u=u)
    t2 = Term.new('dw_point_load(load.val, v)',
                  integral, gamma2, load=load, v=v)
    eq = Equation('balance', t1 - t2)
    eqs = Equations([eq])

    fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({}, lin_solver=ls, status=nls_status)

    pb = Problem('elasticity with shell10x', equations=eqs)
    pb.set_bcs(ebcs=Conditions([fix_u]))
    pb.set_solver(nls)

    state = pb.solve()

    return pb, state, u, gamma2
Exemple #22
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def main():
    from sfepy import data_dir

    parser = OptionParser(usage=usage, version="%prog")
    parser.add_option("-s", "--show", action="store_true", dest="show", default=False, help=help["show"])
    options, args = parser.parse_args()

    mesh = Mesh.from_file(data_dir + "/meshes/2d/rectangle_tri.mesh")
    domain = Domain("domain", mesh)

    min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
    eps = 1e-8 * (max_x - min_x)
    omega = domain.create_region("Omega", "all")
    gamma1 = domain.create_region("Gamma1", "vertices in x < %.10f" % (min_x + eps), "facet")
    gamma2 = domain.create_region("Gamma2", "vertices in x > %.10f" % (max_x - eps), "facet")

    field = Field.from_args("fu", nm.float64, "vector", omega, approx_order=2)

    u = FieldVariable("u", "unknown", field)
    v = FieldVariable("v", "test", field, primary_var_name="u")

    m = Material("m", lam=1.0, mu=1.0)
    f = Material("f", val=[[0.02], [0.01]])

    integral = Integral("i", order=3)

    t1 = Term.new("dw_lin_elastic_iso(m.lam, m.mu, v, u)", integral, omega, m=m, v=v, u=u)
    t2 = Term.new("dw_volume_lvf(f.val, v)", integral, omega, f=f, v=v)
    eq = Equation("balance", t1 + t2)
    eqs = Equations([eq])

    fix_u = EssentialBC("fix_u", gamma1, {"u.all": 0.0})

    bc_fun = Function("shift_u_fun", shift_u_fun, extra_args={"shift": 0.01})
    shift_u = EssentialBC("shift_u", gamma2, {"u.0": bc_fun})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({}, lin_solver=ls, status=nls_status)

    pb = Problem("elasticity", equations=eqs, nls=nls, ls=ls)
    pb.save_regions_as_groups("regions")

    pb.time_update(ebcs=Conditions([fix_u, shift_u]))

    vec = pb.solve()
    print nls_status

    pb.save_state("linear_elasticity.vtk", vec)

    if options.show:
        view = Viewer("linear_elasticity.vtk")
        view(vector_mode="warp_norm", rel_scaling=2, is_scalar_bar=True, is_wireframe=True)
Exemple #23
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    def from_conf(conf, options):
        from sfepy.discrete import FieldVariable, Variables, Problem
        from sfepy.discrete.fem import Mesh, FEDomain, Field

        mesh = Mesh.from_file(data_dir + '/meshes/2d/square_unit_tri.mesh')
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')
        domain.create_region('Left',
                             'vertices in (x < -0.499)',
                             'facet')
        domain.create_region('LeftStrip',
                             'vertices in (x < -0.499)'
                             ' & (y > -0.199) & (y < 0.199)',
                             'facet')
        domain.create_region('LeftFix',
                             'r.Left -v r.LeftStrip',
                             'facet')
        domain.create_region('Right',
                             'vertices in (x > 0.499)',
                             'facet')
        domain.create_region('RightStrip',
                             'vertices in (x > 0.499)'
                             ' & (y > -0.199) & (y < 0.199)',
                             'facet')
        domain.create_region('RightFix',
                             'r.Right -v r.RightStrip',
                             'facet')

        fu = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
        u = FieldVariable('u', 'unknown', fu)

        fp = Field.from_args('fp', nm.float64, 'scalar', omega, approx_order=2)
        p = FieldVariable('p', 'unknown', fp)

        pb = Problem('test', domain=domain, fields=[fu, fp],
                     auto_conf=False, auto_solvers=False)

        test = Test(problem=pb, variables=Variables([u, p]),
                    conf=conf, options=options)
        return test
Exemple #24
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    def from_conf(conf, options):
        mesh = Mesh.from_file('meshes/2d/square_unit_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')

        field = Field.from_args('linear', nm.float64, 'scalar', omega,
                                approx_order=1)

        test = Test(conf=conf, options=options, omega=omega, field=field)
        return test
Exemple #25
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    def from_conf(conf, options):
        mesh = Mesh.from_file('meshes/2d/square_unit_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')

        field = Field.from_args('linear', nm.float64, 'scalar', omega,
                                approx_order=1)

        test = Test(conf=conf, options=options, omega=omega, field=field)
        return test
    def test_evaluate_at(self):
        from sfepy import data_dir
        from sfepy.discrete.fem import Mesh
        from sfepy.discrete import Variables
        from sfepy.discrete.fem import FEDomain, Field

        meshes = {
            'tp': Mesh.from_file(data_dir + '/meshes/3d/block.mesh'),
        }
        datas = gen_datas(meshes)

        fields = {
            'scalar_tp': ((1, 1), 'Omega', 1),
            'vector_tp': ((3, 1), 'Omega', 1),
        }

        ok = True
        for field_name in ['scalar_tp', 'vector_tp']:
            d = FEDomain('d', meshes['tp'])
            d.create_region('Omega', 'all')

            f = fields[field_name]
            field = Field.from_args('f',
                                    nm.complex128,
                                    f[0],
                                    d.regions[f[1]],
                                    approx_order=f[2])
            ff = {field.name: field}

            vv = Variables.from_conf(transform_variables(variables), ff)
            u = vv['u']

            bbox = d.get_mesh_bounding_box()
            t = nm.expand_dims(nm.linspace(0, 1, 100), 1)
            coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0]

            data_r = datas[field_name]
            data_i = 2. / (1 + datas[field_name])

            u.set_from_mesh_vertices(data_r)
            vals_r = u.evaluate_at(coors)
            u.set_from_mesh_vertices(data_i)
            vals_i = u.evaluate_at(coors)
            u.set_from_mesh_vertices(data_r + data_i * 1j)
            vals = u.evaluate_at(coors)

            _ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12)
            _ok = _ok and nm.abs(vals).sum() > 1
            self.report('evaluating complex field %s: %s' % (field_name, _ok))

            ok = ok and _ok

        return ok
def solve_problem(shape, dims, young, poisson, force, transform=None):
    domain = make_domain(dims[:2], shape, transform=transform)

    omega = domain.regions['Omega']
    gamma1 = domain.regions['Gamma1']
    gamma2 = domain.regions['Gamma2']

    field = Field.from_args('fu', nm.float64, 6, omega, approx_order=1,
                            poly_space_base='shell10x')
    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    thickness = dims[2]
    if transform is None:
        pload = [[0.0, 0.0, force / shape[1], 0.0, 0.0, 0.0]] * shape[1]

    elif transform == 'bend':
        pload = [[force / shape[1], 0.0, 0.0, 0.0, 0.0, 0.0]] * shape[1]

    elif transform == 'twist':
        pload = [[0.0, force / shape[1], 0.0, 0.0, 0.0, 0.0]] * shape[1]

    m = Material('m', D=sh.create_elastic_tensor(young=young, poisson=poisson),
                 values={'.drill' : 1e-7})
    load = Material('load', values={'.val' : pload})

    aux = Integral('i', order=3)
    qp_coors, qp_weights = aux.get_qp('3_8')
    qp_coors[:, 2] = thickness * (qp_coors[:, 2] - 0.5)
    qp_weights *= thickness

    integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom')

    t1 = Term.new('dw_shell10x(m.D, m.drill, v, u)',
                  integral, omega, m=m, v=v, u=u)
    t2 = Term.new('dw_point_load(load.val, v)',
                  integral, gamma2, load=load, v=v)
    eq = Equation('balance', t1 - t2)
    eqs = Equations([eq])

    fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({}, lin_solver=ls, status=nls_status)

    pb = Problem('elasticity with shell10x', equations=eqs, nls=nls, ls=ls)
    pb.time_update(ebcs=Conditions([fix_u]))

    state = pb.solve()

    return pb, state, u, gamma2
Exemple #28
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    def test_evaluate_at(self):
        from sfepy import data_dir
        from sfepy.discrete.fem import Mesh
        from sfepy.discrete import Variables
        from sfepy.discrete.fem import FEDomain, Field

        meshes = {
            'tp' : Mesh.from_file(data_dir + '/meshes/3d/block.mesh'),
        }
        datas = gen_datas(meshes)

        fields = {
            'scalar_tp' : ((1,1), 'Omega', 1),
            'vector_tp' : ((3,1), 'Omega', 1),
        }

        ok = True
        for field_name in ['scalar_tp', 'vector_tp']:
            d = FEDomain('d', meshes['tp'])
            d.create_region('Omega', 'all')

            f = fields[field_name]
            field = Field.from_args('f', nm.complex128, f[0],
                                    d.regions[f[1]],
                                    approx_order=f[2])
            ff = {field.name : field}

            vv = Variables.from_conf(transform_variables(variables), ff)
            u = vv['u']

            bbox = d.get_mesh_bounding_box()
            t = nm.expand_dims(nm.linspace(0, 1, 100), 1)
            coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0]

            data_r = datas[field_name]
            data_i = 2. / (1 + datas[field_name])

            u.set_from_mesh_vertices(data_r)
            vals_r = u.evaluate_at(coors)
            u.set_from_mesh_vertices(data_i)
            vals_i = u.evaluate_at(coors)
            u.set_from_mesh_vertices(data_r + data_i * 1j)
            vals = u.evaluate_at(coors)

            _ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12)
            _ok = _ok and nm.abs(vals).sum() > 1
            self.report('evaluating complex field %s: %s' % (field_name, _ok))

            ok = ok and _ok

        return ok
def run(domain, order):
    omega = domain.create_region("Omega", "all")
    bbox = domain.get_mesh_bounding_box()
    min_x, max_x = bbox[:, 0]
    min_y, max_y = bbox[:, 1]
    eps = 1e-8 * (max_x - min_x)
    gamma1 = domain.create_region("Gamma1", "vertices in (x < %.10f)" % (min_x + eps), "facet")
    gamma2 = domain.create_region("Gamma2", "vertices in (x > %.10f)" % (max_x - eps), "facet")
    gamma3 = domain.create_region("Gamma3", "vertices in y < %.10f" % (min_y + eps), "facet")
    gamma4 = domain.create_region("Gamma4", "vertices in y > %.10f" % (max_y - eps), "facet")

    field = Field.from_args("fu", nm.float64, 1, omega, approx_order=order)

    u = FieldVariable("u", "unknown", field)
    v = FieldVariable("v", "test", field, primary_var_name="u")

    integral = Integral("i", order=2 * order)

    t1 = Term.new("dw_laplace(v, u)", integral, omega, v=v, u=u)
    eq = Equation("eq", t1)
    eqs = Equations([eq])

    fix1 = EssentialBC("fix1", gamma1, {"u.0": 0.4})
    fix2 = EssentialBC("fix2", gamma2, {"u.0": 0.0})

    def get_shift(ts, coors, region):
        return nm.ones_like(coors[:, 0])

    dof_map_fun = Function("dof_map_fun", per.match_x_line)
    shift_fun = Function("shift_fun", get_shift)

    sper = LinearCombinationBC(
        "sper", [gamma3, gamma4], {"u.0": "u.0"}, dof_map_fun, "shifted_periodic", arguments=(shift_fun,)
    )

    ls = ScipyDirect({})

    pb = Problem("laplace", equations=eqs, auto_solvers=None)

    pb.time_update(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))

    ev = pb.get_evaluator()
    nls = Newton({}, lin_solver=ls, fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)

    pb.set_solver(nls)

    state = pb.solve()

    return pb, state
Exemple #30
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    def test_projection_tri_quad(self):
        from sfepy.discrete.projections import make_l2_projection

        source = FieldVariable('us', 'unknown', self.field)

        coors = self.field.get_coor()
        vals = nm.sin(2.0 * nm.pi * coors[:, 0] * coors[:, 1])
        source.set_data(vals)

        name = op.join(self.options.out_dir,
                       'test_projection_tri_quad_source.vtk')
        source.save_as_mesh(name)

        mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')

        field = Field.from_args('bilinear',
                                nm.float64,
                                'scalar',
                                omega,
                                approx_order=1)

        target = FieldVariable('ut', 'unknown', field)

        make_l2_projection(target, source)

        name = op.join(self.options.out_dir,
                       'test_projection_tri_quad_target.vtk')
        target.save_as_mesh(name)

        bbox = self.field.domain.get_mesh_bounding_box()
        x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
        y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)

        xx, yy = nm.meshgrid(x, y)
        test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()

        vec1 = source.evaluate_at(test_coors)
        vec2 = target.evaluate_at(test_coors)

        ok = (nm.abs(vec1 - vec2) < 0.01).all()

        return ok
Exemple #31
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    def test_invariance_qp(self):
        from sfepy import data_dir
        from sfepy.discrete import Variables, Integral
        from sfepy.discrete.fem import Mesh, FEDomain, Field
        from sfepy.terms import Term
        from sfepy.discrete.common.mappings import get_physical_qps

        mesh = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')

        bbox = mesh.get_bounding_box()
        dd = bbox[1,:] - bbox[0,:]
        data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])

        variables = {
            'u'       : ('unknown field', 'scalar_tp', 0),
            'v'       : ('test field',    'scalar_tp', 'u'),
        }

        domain = FEDomain('domain', mesh)
        omega = domain.create_region('Omega', 'all')
        field = Field.from_args('scalar_tp', nm.float64, 1, omega,
                                approx_order=1)
        ff = {field.name : field}

        vv = Variables.from_conf(transform_variables(variables), ff)
        u = vv['u']
        u.set_from_mesh_vertices(data)

        integral = Integral('i', order=2)
        term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
        term.setup()
        val1 = term.evaluate(mode='qp')
        val1 = val1.ravel()

        qps = get_physical_qps(omega, integral)
        coors = qps.values

        val2 = u.evaluate_at(coors).ravel()

        self.report('max. difference:', nm.abs(val1 - val2).max())
        ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
        self.report('invariance in qp: %s' % ok)

        return ok
Exemple #32
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def prepare_variable(filename, n_components):
    from sfepy.discrete import FieldVariable
    from sfepy.discrete.fem import Mesh, FEDomain, Field

    mesh = Mesh.from_file(filename)

    bbox = mesh.get_bounding_box()
    dd = bbox[1, :] - bbox[0, :]
    data = nm.sin(4.0 * nm.pi * mesh.coors[:, 0:1] / dd[0]) * nm.cos(4.0 * nm.pi * mesh.coors[:, 1:2] / dd[1])

    domain = FEDomain("domain", mesh)
    omega = domain.create_region("Omega", "all")
    field = Field.from_args("field", nm.float64, n_components, omega, approx_order=2)

    u = FieldVariable("u", "parameter", field, primary_var_name="(set-to-None)")
    u.set_from_mesh_vertices(data * nm.arange(1, n_components + 1)[None, :])

    return u
Exemple #33
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    def test_projection_tri_quad(self):
        from sfepy.discrete.projections import make_l2_projection

        source = FieldVariable('us', 'unknown', self.field)

        coors = self.field.get_coor()
        vals = nm.sin(2.0 * nm.pi * coors[:,0] * coors[:,1])
        source.set_data(vals)

        name = op.join(self.options.out_dir,
                       'test_projection_tri_quad_source.vtk')
        source.save_as_mesh(name)

        mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = FEDomain('domain', mesh)

        omega = domain.create_region('Omega', 'all')


        field = Field.from_args('bilinear', nm.float64, 'scalar', omega,
                                approx_order=1)

        target = FieldVariable('ut', 'unknown', field)

        make_l2_projection(target, source)

        name = op.join(self.options.out_dir,
                       'test_projection_tri_quad_target.vtk')
        target.save_as_mesh(name)

        bbox = self.field.domain.get_mesh_bounding_box()
        x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
        y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)

        xx, yy = nm.meshgrid(x, y)
        test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()

        vec1 = source.evaluate_at(test_coors)
        vec2 = target.evaluate_at(test_coors)

        ok = (nm.abs(vec1 - vec2) < 0.01).all()

        return ok
Exemple #34
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def prepare_variable(filename, n_components):
    from sfepy.discrete import FieldVariable
    from sfepy.discrete.fem import Mesh, FEDomain, Field

    mesh = Mesh.from_file(filename)

    bbox = mesh.get_bounding_box()
    dd = bbox[1,:] - bbox[0,:]
    data = (nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0])
            * nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1]))

    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('field', nm.float64, n_components, omega,
                            approx_order=2)

    u = FieldVariable('u', 'parameter', field,
                      primary_var_name='(set-to-None)')
    u.set_from_mesh_vertices(nm.c_[tuple([data] * n_components)])

    return u
Exemple #35
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def linear_projection(pb, cval):
    from sfepy.discrete import (FieldVariable, Material, Integral, Equation,
                                Equations, Problem)
    from sfepy.discrete.fem import Mesh, FEDomain, Field
    from sfepy.terms import Term
    from sfepy.solvers.ls import ScipyDirect
    from sfepy.solvers.nls import Newton
    from sfepy.base.base import IndexedStruct

    mesh = Mesh.from_file(pb.conf.filename_mesh)
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('scf', nm.float64, 'scalar', omega, approx_order=1)

    g = FieldVariable('g', 'unknown', field)
    f = FieldVariable('f', 'test', field, primary_var_name='g')

    integral = Integral('i', order=2)
    m = Material('m', function=set_grad)

    t1 = Term.new('dw_volume_dot(f, g)', integral, omega, f=f, g=g)
    t2 = Term.new('dw_volume_lvf(m.cs, f)', integral, omega, m=m, f=f)
    eq = Equation('balance', t1 - t2)
    eqs = Equations([eq])
    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({'eps_a': 1e-15}, lin_solver=ls, status=nls_status)
    pb = Problem('elasticity', equations=eqs)
    pb.set_solver(nls)

    out = nm.empty((g.n_dof, cval.shape[2]), dtype=nm.float64)
    for ii in range(cval.shape[2]):
        pb.data = nm.ascontiguousarray(cval[:, :, ii, :])
        pb.time_update()
        state = pb.solve()
        out[:, ii] = state.get_parts()['g']

    return out
def verify_save_dof_maps(field,
                         cell_tasks,
                         dof_maps,
                         id_map,
                         options,
                         verbose=False):
    vec = pl.verify_task_dof_maps(dof_maps, id_map, field, verbose=verbose)

    order = options.order
    mesh = field.domain.mesh

    sfield = Field.from_args('aux',
                             nm.float64,
                             'scalar',
                             field.region,
                             approx_order=order)
    aux = FieldVariable('aux',
                        'parameter',
                        sfield,
                        primary_var_name='(set-to-None)')
    out = aux.create_output(vec,
                            linearization=Struct(kind='adaptive',
                                                 min_level=order - 1,
                                                 max_level=order - 1,
                                                 eps=1e-8))

    filename = os.path.join(options.output_dir, 'para-domains-dofs.h5')
    if field.is_higher_order():
        out['aux'].mesh.write(filename, out=out)

    else:
        mesh.write(filename, out=out)

    out = Struct(name='cells',
                 mode='cell',
                 data=cell_tasks[:, None, None, None])
    filename = os.path.join(options.output_dir, 'para-domains-cells.h5')
    mesh.write(filename, out={'cells': out})
Exemple #37
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    def test_project_tensors(self):
        from sfepy.discrete import FieldVariable
        from sfepy.discrete.projections import project_by_component

        ok = True

        u = FieldVariable('u', 'parameter', self.field,
                          primary_var_name='(set-to-None)')
        u.set_constant(1.0)

        component = FieldVariable('component', 'parameter', self.field,
                                  primary_var_name='(set-to-None)')

        nls_options = {'eps_a' : 1e-16, 'i_max' : 1}

        u_qp = u.evaluate()
        u2 = FieldVariable('u2', 'parameter', self.field,
                           primary_var_name='(set-to-None)')
        project_by_component(u2, u_qp, component, self.field.approx_order,
                             nls_options=nls_options)

        _ok = self.compare_vectors(u(), u2())
        ok = ok and _ok

        gu_qp = u.evaluate(mode='grad')

        gfield = Field.from_args('gu', nm.float64, 2, self.field.region,
                                 approx_order=self.field.approx_order)
        gu = FieldVariable('gu', 'parameter', gfield,
                           primary_var_name='(set-to-None)')

        project_by_component(gu, gu_qp, component, gfield.approx_order,
                             nls_options=nls_options)

        _ok = self.compare_vectors(gu(), nm.zeros_like(gu()))
        ok = ok and _ok

        return ok
Exemple #38
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def get_fields(shape, delta_x):
    """Get the fields for the displacement and test function

    Args:
      shape: the shape of the domain
      delta_x: the mesh spacing

    Returns:
      tuple of field variables
    """
    return pipe(
        np.array(shape),
        lambda x: gen_block_mesh(
            x * delta_x, x + 1, np.zeros_like(shape), verbose=False
        ),
        lambda x: Domain("domain", x),
        lambda x: x.create_region("region_all", "all"),
        lambda x: Field.from_args("fu", np.float64, "vector", x, approx_order=2),
        lambda x: (
            FieldVariable("u", "unknown", x),
            FieldVariable("v", "test", x, primary_var_name="u"),
        ),
    )
    def test_linearization(self):
        from sfepy.base.base import Struct
        from sfepy.discrete.fem import Mesh, FEDomain, Field
        from sfepy import data_dir

        geometries = ['2_3', '2_4', '3_4', '3_8']
        approx_orders = [1, 2]
        funs = [nm.cos, nm.sin, lambda x: x]

        ok = True
        for geometry in geometries:
            name = os.path.join(data_dir,
                                'meshes/elements/%s_1.mesh' % geometry)
            mesh = Mesh.from_file(name)

            domain = FEDomain('', mesh)
            domain = domain.refine()

            domain.mesh.write(self.join('linearizer-%s-0.mesh' % geometry))

            omega = domain.create_region('Omega', 'all')

            for approx_order in approx_orders:
                for dpn in [1, mesh.dim]:
                    self.report('geometry: %s, approx. order: %d, dpn: %d' %
                                (geometry, approx_order, dpn))

                    field = Field.from_args('fu',
                                            nm.float64,
                                            dpn,
                                            omega,
                                            approx_order=approx_order)

                    cc = field.get_coor()
                    dofs = nm.zeros((field.n_nod, dpn), dtype=nm.float64)

                    for ic in range(dpn):
                        dofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    vmesh, vdofs, level = field.linearize(dofs,
                                                          min_level=0,
                                                          max_level=3,
                                                          eps=1e-2)

                    if approx_order == 1:
                        _ok = level == 0

                    else:
                        _ok = level > 0
                    self.report('max. refinement level: %d: %s' % (level, _ok))

                    ok = ok and _ok

                    rdofs = nm.zeros((vmesh.n_nod, dpn), dtype=nm.float64)
                    cc = vmesh.coors
                    for ic in range(dpn):
                        rdofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    _ok = nm.allclose(rdofs, vdofs, rtol=0.0, atol=0.03)
                    self.report('interpolation: %s' % _ok)
                    ok = ok and _ok

                    out = {
                        'u':
                        Struct(name='output_data',
                               mode='vertex',
                               data=vdofs,
                               var_name='u',
                               dofs=None)
                    }

                    name = self.join('linearizer-%s-%d-%d' %
                                     (geometry, approx_order, dpn))

                    vmesh.write(name + '.mesh')
                    vmesh.write(name + '.vtk', out=out)

        return ok
def create_local_problem(omega_gi, order):
    """
    Local problem definition using a domain corresponding to the global region
    `omega_gi`.
    """
    mesh = omega_gi.domain.mesh

    # All tasks have the whole mesh.
    bbox = mesh.get_bounding_box()
    min_x, max_x = bbox[:, 0]
    eps_x = 1e-8 * (max_x - min_x)

    mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
    domain_i = FEDomain('domain_i', mesh_i)
    omega_i = domain_i.create_region('Omega', 'all')

    gamma1_i = domain_i.create_region('Gamma1',
                                      'vertices in (x < %.10f)' %
                                      (min_x + eps_x),
                                      'facet',
                                      allow_empty=True)
    gamma2_i = domain_i.create_region('Gamma2',
                                      'vertices in (x > %.10f)' %
                                      (max_x - eps_x),
                                      'facet',
                                      allow_empty=True)

    field_i = Field.from_args('fu', nm.float64, 1, omega_i, approx_order=order)

    output('number of local field DOFs:', field_i.n_nod)

    u_i = FieldVariable('u_i', 'unknown', field_i)
    v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')

    integral = Integral('i', order=2 * order)

    mat = Material('m', lam=10, mu=5)
    t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
                  integral,
                  omega_i,
                  m=mat,
                  v_i=v_i,
                  u_i=u_i)

    def _get_load(coors):
        val = nm.ones_like(coors[:, 0])
        for coor in coors.T:
            val *= nm.sin(4 * nm.pi * coor)
        return val

    def get_load(ts, coors, mode=None, **kwargs):
        if mode == 'qp':
            return {'val': _get_load(coors).reshape(coors.shape[0], 1, 1)}

    load = Material('load', function=Function('get_load', get_load))

    t2 = Term.new('dw_volume_lvf(load.val, v_i)',
                  integral,
                  omega_i,
                  load=load,
                  v_i=v_i)

    eq = Equation('balance', t1 - 100 * t2)
    eqs = Equations([eq])

    ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all': 0.0})
    ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all': 0.1})

    pb = Problem('problem_i', equations=eqs, active_only=False)
    pb.time_update(ebcs=Conditions([ebc1, ebc2]))
    pb.update_materials()

    return pb
def main():
    from sfepy import data_dir

    parser = OptionParser(usage=usage, version='%prog')
    parser.add_option('--diffusivity',
                      metavar='float',
                      type=float,
                      action='store',
                      dest='diffusivity',
                      default=1e-5,
                      help=helps['diffusivity'])
    parser.add_option('--ic-max',
                      metavar='float',
                      type=float,
                      action='store',
                      dest='ic_max',
                      default=2.0,
                      help=helps['ic_max'])
    parser.add_option('--order',
                      metavar='int',
                      type=int,
                      action='store',
                      dest='order',
                      default=2,
                      help=helps['order'])
    parser.add_option('-r',
                      '--refine',
                      metavar='int',
                      type=int,
                      action='store',
                      dest='refine',
                      default=0,
                      help=helps['refine'])
    parser.add_option('-p',
                      '--probe',
                      action="store_true",
                      dest='probe',
                      default=False,
                      help=helps['probe'])
    parser.add_option('-s',
                      '--show',
                      action="store_true",
                      dest='show',
                      default=False,
                      help=helps['show'])
    options, args = parser.parse_args()

    assert_((0 < options.order),
            'temperature approximation order must be at least 1!')

    output('using values:')
    output('  diffusivity:', options.diffusivity)
    output('  max. IC value:', options.ic_max)
    output('uniform mesh refinement level:', options.refine)

    mesh = Mesh.from_file(data_dir + '/meshes/3d/cylinder.mesh')
    domain = FEDomain('domain', mesh)

    if options.refine > 0:
        for ii in xrange(options.refine):
            output('refine %d...' % ii)
            domain = domain.refine()
            output('... %d nodes %d elements' %
                   (domain.shape.n_nod, domain.shape.n_el))

    omega = domain.create_region('Omega', 'all')
    left = domain.create_region('Left', 'vertices in x < 0.00001', 'facet')
    right = domain.create_region('Right', 'vertices in x > 0.099999', 'facet')

    field = Field.from_args('fu',
                            nm.float64,
                            'scalar',
                            omega,
                            approx_order=options.order)

    T = FieldVariable('T', 'unknown', field, history=1)
    s = FieldVariable('s', 'test', field, primary_var_name='T')

    m = Material('m', diffusivity=options.diffusivity * nm.eye(3))

    integral = Integral('i', order=2 * options.order)

    t1 = Term.new('dw_diffusion(m.diffusivity, s, T)',
                  integral,
                  omega,
                  m=m,
                  s=s,
                  T=T)
    t2 = Term.new('dw_volume_dot(s, dT/dt)', integral, omega, s=s, T=T)
    eq = Equation('balance', t1 + t2)
    eqs = Equations([eq])

    # Boundary conditions.
    ebc1 = EssentialBC('T1', left, {'T.0': 2.0})
    ebc2 = EssentialBC('T2', right, {'T.0': -2.0})

    # Initial conditions.
    def get_ic(coors, ic):
        x, y, z = coors.T
        return 2 - 40.0 * x + options.ic_max * nm.sin(4 * nm.pi * x / 0.1)

    ic_fun = Function('ic_fun', get_ic)
    ic = InitialCondition('ic', omega, {'T.0': ic_fun})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({'is_linear': True}, lin_solver=ls, status=nls_status)

    pb = Problem('heat', equations=eqs, nls=nls, ls=ls)
    pb.set_bcs(ebcs=Conditions([ebc1, ebc2]))
    pb.set_ics(Conditions([ic]))

    tss = SimpleTimeSteppingSolver({
        't0': 0.0,
        't1': 100.0,
        'n_step': 11
    },
                                   problem=pb)
    tss.init_time()

    if options.probe:
        # Prepare probe data.
        probes, labels = gen_lines(pb)

        ev = pb.evaluate
        order = 2 * (options.order - 1)

        gfield = Field.from_args('gu',
                                 nm.float64,
                                 'vector',
                                 omega,
                                 approx_order=options.order - 1)
        dvel = FieldVariable('dvel',
                             'parameter',
                             gfield,
                             primary_var_name='(set-to-None)')
        cfield = Field.from_args('gu',
                                 nm.float64,
                                 'scalar',
                                 omega,
                                 approx_order=options.order - 1)
        component = FieldVariable('component',
                                  'parameter',
                                  cfield,
                                  primary_var_name='(set-to-None)')

        nls_options = {'eps_a': 1e-16, 'i_max': 1}

        if options.show:
            plt.ion()

    # Solve the problem using the time stepping solver.
    suffix = tss.ts.suffix
    for step, time, state in tss():
        if options.probe:
            # Probe the solution.
            dvel_qp = ev('ev_diffusion_velocity.%d.Omega(m.diffusivity, T)' %
                         order,
                         copy_materials=False,
                         mode='qp')
            project_by_component(dvel,
                                 dvel_qp,
                                 component,
                                 order,
                                 nls_options=nls_options)

            all_results = []
            for ii, probe in enumerate(probes):
                fig, results = probe_results(ii, T, dvel, probe, labels[ii])

                all_results.append(results)

            plt.tight_layout()
            fig.savefig('time_poisson_interactive_probe_%s.png' %
                        (suffix % step),
                        bbox_inches='tight')

            if options.show:
                plt.draw()

            for ii, results in enumerate(all_results):
                output('probe %d (%s):' % (ii, probes[ii].name))
                output.level += 2
                for key, res in ordered_iteritems(results):
                    output(key + ':')
                    val = res[1]
                    output('  min: %+.2e, mean: %+.2e, max: %+.2e' %
                           (val.min(), val.mean(), val.max()))
                output.level -= 2
Exemple #42
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def solve_problem(mesh_filename, options, comm):
    order_u = options.order_u
    order_p = options.order_p

    rank, size = comm.Get_rank(), comm.Get_size()

    output('rank', rank, 'of', size)

    stats = Struct()
    timer = Timer('solve_timer')

    timer.start()
    mesh = Mesh.from_file(mesh_filename)
    stats.t_read_mesh = timer.stop()

    timer.start()
    if rank == 0:
        cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
                                       verbose=True)

    else:
        cell_tasks = None

    stats.t_partition_mesh = timer.stop()

    output('creating global domain and fields...')
    timer.start()

    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field1 = Field.from_args('fu', nm.float64, mesh.dim, omega,
                             approx_order=order_u)
    field2 = Field.from_args('fp', nm.float64, 1, omega,
                             approx_order=order_p)
    fields = [field1, field2]

    stats.t_create_global_fields = timer.stop()
    output('...done in', timer.dt)

    output('distributing fields...')
    timer.start()

    distribute = pl.distribute_fields_dofs
    lfds, gfds = distribute(fields, cell_tasks,
                            is_overlap=True,
                            use_expand_dofs=True,
                            save_inter_regions=options.save_inter_regions,
                            output_dir=options.output_dir,
                            comm=comm, verbose=True)

    stats.t_distribute_fields_dofs = timer.stop()
    output('...done in', timer.dt)

    output('creating local problem...')
    timer.start()

    cells = lfds[0].cells

    omega_gi = Region.from_cells(cells, domain)
    omega_gi.finalize()
    omega_gi.update_shape()

    pb = create_local_problem(omega_gi, [order_u, order_p])

    variables = pb.get_variables()

    state = State(variables)
    state.fill(0.0)
    state.apply_ebc()

    stats.t_create_local_problem = timer.stop()
    output('...done in', timer.dt)

    output('allocating global system...')
    timer.start()

    sizes, drange, pdofs = pl.setup_composite_dofs(lfds, fields, variables,
                                                   verbose=True)
    pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
                                              is_overlap=True, comm=comm,
                                              verbose=True)

    stats.t_allocate_global_system = timer.stop()
    output('...done in', timer.dt)

    output('creating solver...')
    timer.start()

    conf = Struct(method='bcgsl', precond='jacobi', sub_precond='none',
                  i_max=10000, eps_a=1e-50, eps_r=1e-6, eps_d=1e4,
                  verbose=True)
    status = {}
    ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)

    field_ranges = {}
    for ii, variable in enumerate(variables.iter_state(ordered=True)):
        field_ranges[variable.name] = lfds[ii].petsc_dofs_range

    ls.set_field_split(field_ranges, comm=comm)

    ev = PETScParallelEvaluator(pb, pdofs, drange, True,
                                psol, comm, verbose=True)

    nls_status = {}
    conf = Struct(method='newtonls',
                  i_max=5, eps_a=0, eps_r=1e-5, eps_s=0.0,
                  verbose=True)
    nls = PETScNonlinearSolver(conf, pmtx=pmtx, prhs=prhs, comm=comm,
                               fun=ev.eval_residual,
                               fun_grad=ev.eval_tangent_matrix,
                               lin_solver=ls, status=nls_status)

    stats.t_create_solver = timer.stop()
    output('...done in', timer.dt)

    output('solving...')
    timer.start()

    state = pb.create_state()
    state.apply_ebc()

    ev.psol_i[...] = state()
    ev.gather(psol, ev.psol_i)

    psol = nls(psol)

    ev.scatter(ev.psol_i, psol)
    sol0_i = ev.psol_i[...]

    stats.t_solve = timer.stop()
    output('...done in', timer.dt)

    output('saving solution...')
    timer.start()

    state.set_full(sol0_i)
    out = state.create_output_dict()

    filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
    pb.domain.mesh.write(filename, io='auto', out=out)

    gather_to_zero = pl.create_gather_to_zero(psol)

    psol_full = gather_to_zero(psol)

    if comm.rank == 0:
        sol = psol_full[...].copy()

        u = FieldVariable('u', 'parameter', field1,
                          primary_var_name='(set-to-None)')
        remap = gfds[0].id_map
        ug = sol[remap]

        p = FieldVariable('p', 'parameter', field2,
                          primary_var_name='(set-to-None)')
        remap = gfds[1].id_map
        pg = sol[remap]

        if (((order_u == 1) and (order_p == 1))
            or (options.linearization == 'strip')):
            out = u.create_output(ug)
            out.update(p.create_output(pg))
            filename = os.path.join(options.output_dir, 'sol.h5')
            mesh.write(filename, io='auto', out=out)

        else:
            out = u.create_output(ug, linearization=Struct(kind='adaptive',
                                                           min_level=0,
                                                           max_level=order_u,
                                                           eps=1e-3))

            filename = os.path.join(options.output_dir, 'sol_u.h5')
            out['u'].mesh.write(filename, io='auto', out=out)

            out = p.create_output(pg, linearization=Struct(kind='adaptive',
                                                           min_level=0,
                                                           max_level=order_p,
                                                           eps=1e-3))

            filename = os.path.join(options.output_dir, 'sol_p.h5')
            out['p'].mesh.write(filename, io='auto', out=out)

    stats.t_save_solution = timer.stop()
    output('...done in', timer.dt)

    stats.t_total = timer.total

    stats.n_dof = sizes[1]
    stats.n_dof_local = sizes[0]
    stats.n_cell = omega.shape.n_cell
    stats.n_cell_local = omega_gi.shape.n_cell

    return stats
def solve_problem(mesh_filename, options, comm):
    order_u = options.order_u
    order_p = options.order_p

    rank, size = comm.Get_rank(), comm.Get_size()

    output('rank', rank, 'of', size)

    mesh = Mesh.from_file(mesh_filename)

    if rank == 0:
        cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
                                       verbose=True)

    else:
        cell_tasks = None

    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field1 = Field.from_args('fu', nm.float64, mesh.dim, omega,
                             approx_order=order_u)
    field2 = Field.from_args('fp', nm.float64, 1, omega,
                             approx_order=order_p)
    fields = [field1, field2]

    output('distributing fields...')
    tt = time.clock()

    lfds, gfds = pl.distribute_fields_dofs(fields, cell_tasks,
                                           is_overlap=True,
                                           use_expand_dofs=True,
                                           comm=comm, verbose=True)

    output('...done in', time.clock() - tt)

    output('creating local problem...')
    tt = time.clock()

    cells = lfds[0].cells

    omega_gi = Region.from_cells(cells, domain)
    omega_gi.finalize()
    omega_gi.update_shape()

    pb = create_local_problem(omega_gi, [order_u, order_p])

    variables = pb.get_variables()

    state = State(variables)
    state.fill(0.0)
    state.apply_ebc()

    output('...done in', time.clock() - tt)


    output('allocating global system...')
    tt = time.clock()

    sizes, drange, pdofs = pl.setup_composite_dofs(lfds, fields, variables,
                                                   verbose=True)
    pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
                                              is_overlap=True, comm=comm,
                                              verbose=True)

    output('...done in', time.clock() - tt)

    output('creating solver...')
    tt = time.clock()

    conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
                  i_max=10000, eps_a=1e-50, eps_r=1e-6, eps_d=1e4,
                  verbose=True)
    status = {}
    ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)

    field_ranges = {}
    for ii, variable in enumerate(variables.iter_state(ordered=True)):
        field_ranges[variable.name] = lfds[ii].petsc_dofs_range

    ls.set_field_split(field_ranges, comm=comm)

    ev = PETScParallelEvaluator(pb, pdofs, drange, True,
                                psol, comm, verbose=True)

    nls_status = {}
    conf = Struct(method='newtonls',
                  i_max=5, eps_a=0, eps_r=1e-5, eps_s=0.0,
                  verbose=True)
    nls = PETScNonlinearSolver(conf, pmtx=pmtx, prhs=prhs, comm=comm,
                               fun=ev.eval_residual,
                               fun_grad=ev.eval_tangent_matrix,
                               lin_solver=ls, status=nls_status)

    output('...done in', time.clock() - tt)

    output('solving...')
    tt = time.clock()

    state = pb.create_state()
    state.apply_ebc()

    ev.psol_i[...] = state()
    ev.gather(psol, ev.psol_i)

    psol = nls(psol)

    ev.scatter(ev.psol_i, psol)
    sol0_i = ev.psol_i[...]

    output('...done in', time.clock() - tt)

    output('saving solution...')
    tt = time.clock()

    state.set_full(sol0_i)
    out = state.create_output_dict()

    filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
    pb.domain.mesh.write(filename, io='auto', out=out)

    gather_to_zero = pl.create_gather_to_zero(psol)

    psol_full = gather_to_zero(psol)

    if comm.rank == 0:
        sol = psol_full[...].copy()

        u = FieldVariable('u', 'parameter', field1,
                          primary_var_name='(set-to-None)')
        remap = gfds[0].id_map
        ug = sol[remap]

        p = FieldVariable('p', 'parameter', field2,
                          primary_var_name='(set-to-None)')
        remap = gfds[1].id_map
        pg = sol[remap]

        if (((order_u == 1) and (order_p == 1))
            or (options.linearization == 'strip')):
            out = u.create_output(ug)
            out.update(p.create_output(pg))
            filename = os.path.join(options.output_dir, 'sol.h5')
            mesh.write(filename, io='auto', out=out)

        else:
            out = u.create_output(ug, linearization=Struct(kind='adaptive',
                                                           min_level=0,
                                                           max_level=order_u,
                                                           eps=1e-3))

            filename = os.path.join(options.output_dir, 'sol_u.h5')
            out['u'].mesh.write(filename, io='auto', out=out)

            out = p.create_output(pg, linearization=Struct(kind='adaptive',
                                                           min_level=0,
                                                           max_level=order_p,
                                                           eps=1e-3))

            filename = os.path.join(options.output_dir, 'sol_p.h5')
            out['p'].mesh.write(filename, io='auto', out=out)

    output('...done in', time.clock() - tt)
Exemple #44
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    def test_linearization(self):
        from sfepy.base.base import Struct
        from sfepy.discrete.fem import Mesh, FEDomain, Field
        from sfepy import data_dir

        geometries = ['2_3', '2_4', '3_4', '3_8']
        approx_orders = [1, 2]
        funs = [nm.cos, nm.sin, lambda x: x]

        ok = True
        for geometry in geometries:
            name = os.path.join(data_dir,
                                'meshes/elements/%s_1.mesh' % geometry)
            mesh = Mesh.from_file(name)

            domain = FEDomain('', mesh)
            domain = domain.refine()

            domain.mesh.write(self.join('linearizer-%s-0.mesh' % geometry))

            omega = domain.create_region('Omega', 'all')

            for approx_order in approx_orders:
                for dpn in [1, mesh.dim]:
                    self.report('geometry: %s, approx. order: %d, dpn: %d' %
                                (geometry, approx_order, dpn))

                    field = Field.from_args('fu', nm.float64, dpn, omega,
                                            approx_order=approx_order)

                    cc = field.get_coor()
                    dofs = nm.zeros((field.n_nod, dpn), dtype=nm.float64)

                    for ic in range(dpn):
                        dofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    vmesh, vdofs, level = field.linearize(dofs,
                                                          min_level=0,
                                                          max_level=3,
                                                          eps=1e-2)

                    if approx_order == 1:
                        _ok = level == 0

                    else:
                        _ok = level > 0
                    self.report('max. refinement level: %d: %s' % (level, _ok))

                    ok = ok and _ok

                    rdofs = nm.zeros((vmesh.n_nod, dpn), dtype=nm.float64)
                    cc = vmesh.coors
                    for ic in range(dpn):
                        rdofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))

                    _ok = nm.allclose(rdofs, vdofs, rtol=0.0, atol=0.03)
                    self.report('interpolation: %s' % _ok)
                    ok = ok and _ok

                    out = {
                        'u' : Struct(name='output_data',
                                     mode='vertex', data=vdofs,
                                     var_name='u', dofs=None)
                    }

                    name = self.join('linearizer-%s-%d-%d'
                                     % (geometry, approx_order, dpn))

                    vmesh.write(name + '.mesh')
                    vmesh.write(name + '.vtk', out=out)

        return ok
Exemple #45
0
    def _eval_basis_transform(self, subs):
        """
        """
        from sfepy.discrete import Integral
        from sfepy.discrete.fem import Mesh, FEDomain, Field

        transform = nm.tile(nm.eye(self.econn.shape[1]),
                            (self.econn.shape[0], 1, 1))
        if subs is None:
            return transform

        gel = self.gel
        ao = self.approx_order

        conn = [gel.conn]
        mesh = Mesh.from_data('a', gel.coors, None, [conn], [nm.array([0])],
                              [gel.name])
        cdomain = FEDomain('d', mesh)
        comega = cdomain.create_region('Omega', 'all')
        rcfield = Field.from_args('rc', self.dtype, 1, comega, approx_order=ao)

        fdomain = cdomain.refine()
        fomega = fdomain.create_region('Omega', 'all')
        rffield = Field.from_args('rf', self.dtype, 1, fomega, approx_order=ao)

        def assign_transform(transform, bf, subs, ef):
            if not len(subs): return

            n_sub = (subs.shape[1] - 2) // 2

            for ii, sub in enumerate(subs):
                for ij in range(n_sub):
                    ik = 2 * (ij + 1)

                    fface = ef[sub[ik + 1]]

                    mtx = transform[sub[ik]]
                    ix, iy = nm.meshgrid(fface, fface)

                    cbf = bf[iy, 0, ix]

                    mtx[ix, iy] = cbf

        fcoors = rffield.get_coor()

        coors = fcoors[rffield.econn[0]]
        integral = Integral('i',
                            coors=coors,
                            weights=nm.ones_like(coors[:, 0]))

        rcfield.clear_qp_base()
        bf = rcfield.get_base('v', False, integral)

        if gel.name == '2_4':
            fsubs = subs
            esubs = None

            assign_transform(transform, bf, fsubs, rffield.efaces)

        else:
            fsubs = subs[0]
            esubs = subs[1]

            assign_transform(transform, bf, fsubs, rffield.efaces)
            if esubs is not None:
                assign_transform(transform, bf, esubs, rffield.eedges)

        assert_((nm.abs(transform.sum(1) - 1.0) < 1e-15).all())

        return transform
def make_term_args(arg_shapes,
                   arg_kinds,
                   arg_types,
                   ats_mode,
                   domain,
                   material_value=None,
                   poly_space_base=None):
    from sfepy.base.base import basestr
    from sfepy.discrete import FieldVariable, Material, Variables, Materials
    from sfepy.discrete.fem import Field
    from sfepy.solvers.ts import TimeStepper
    from sfepy.mechanics.tensors import dim2sym

    omega = domain.regions['Omega']
    dim = domain.shape.dim
    sym = dim2sym(dim)

    def _parse_scalar_shape(sh):
        if isinstance(sh, basestr):
            if sh == 'D':
                return dim

            elif sh == 'S':
                return sym

            elif sh == 'N':  # General number ;)
                return 1

            else:
                return int(sh)

        else:
            return sh

    def _parse_tuple_shape(sh):
        if isinstance(sh, basestr):
            return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]

        else:
            return (int(sh), )

    args = {}
    str_args = []
    materials = []
    variables = []
    for ii, arg_kind in enumerate(arg_kinds):
        if arg_kind != 'ts':
            if ats_mode is not None:
                extended_ats = arg_types[ii] + ('/%s' % ats_mode)

            else:
                extended_ats = arg_types[ii]

            try:
                sh = arg_shapes[arg_types[ii]]

            except KeyError:
                sh = arg_shapes[extended_ats]

        if arg_kind.endswith('variable'):
            shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
            field = Field.from_args('f%d' % ii,
                                    nm.float64,
                                    shape,
                                    omega,
                                    approx_order=1,
                                    poly_space_base=poly_space_base)

            if arg_kind == 'virtual_variable':
                if sh[1] is not None:
                    istate = arg_types.index(sh[1])

                else:
                    # Only virtual variable in arguments.
                    istate = -1
                    # -> Make fake variable.
                    var = FieldVariable('u-1', 'unknown', field)
                    var.set_constant(0.0)
                    variables.append(var)

                var = FieldVariable('v',
                                    'test',
                                    field,
                                    primary_var_name='u%d' % istate)

            elif arg_kind == 'state_variable':
                var = FieldVariable('u%d' % ii, 'unknown', field)
                var.set_constant(0.0)

            elif arg_kind == 'parameter_variable':
                var = FieldVariable('p%d' % ii,
                                    'parameter',
                                    field,
                                    primary_var_name='(set-to-None)')
                var.set_constant(0.0)

            variables.append(var)
            str_args.append(var.name)
            args[var.name] = var

        elif arg_kind.endswith('material'):
            if sh is None:  # Switched-off opt_material.
                continue

            prefix = ''
            if isinstance(sh, basestr):
                aux = sh.split(':')
                if len(aux) == 2:
                    prefix, sh = aux

            if material_value is None:
                material_value = 1.0

            shape = _parse_tuple_shape(sh)
            if (len(shape) > 1) or (shape[0] > 1):
                if ((len(shape) == 2) and (shape[0] == shape[1])
                        and (material_value != 0.0)):
                    # Identity matrix.
                    val = nm.eye(shape[0], dtype=nm.float64)

                else:
                    # Array.
                    val = nm.empty(shape, dtype=nm.float64)
                    val.fill(material_value)

                values = {'%sc%d' % (prefix, ii): val}

            elif (len(shape) == 1) and (shape[0] == 1):
                # Single scalar as a special value.
                values = {'.c%d' % ii: material_value}

            else:
                raise ValueError('wrong material shape! (%s)' % shape)

            mat = Material('m%d' % ii, values=values)

            materials.append(mat)
            str_args.append(mat.name + '.' + 'c%d' % ii)
            args[mat.name] = mat

        elif arg_kind == 'ts':
            ts = TimeStepper(0.0, 1.0, 1.0, 5)
            str_args.append('ts')
            args['ts'] = ts

        else:
            str_args.append('user%d' % ii)
            args[str_args[-1]] = None

    materials = Materials(materials)
    variables = Variables(variables)

    return args, str_args, materials, variables
def main():
    parser = ArgumentParser(description=__doc__.rstrip(),
                            formatter_class=RawDescriptionHelpFormatter)
    parser.add_argument('output_dir', help=helps['output_dir'])
    parser.add_argument('--dims', metavar='dims',
                        action='store', dest='dims',
                        default='1.0,1.0,1.0', help=helps['dims'])
    parser.add_argument('--shape', metavar='shape',
                        action='store', dest='shape',
                        default='7,7,7', help=helps['shape'])
    parser.add_argument('--centre', metavar='centre',
                        action='store', dest='centre',
                        default='0.0,0.0,0.0', help=helps['centre'])
    parser.add_argument('-3', '--3d',
                        action='store_true', dest='is_3d',
                        default=False, help=helps['3d'])
    parser.add_argument('--order', metavar='int', type=int,
                        action='store', dest='order',
                        default=1, help=helps['order'])
    options = parser.parse_args()

    dim = 3 if options.is_3d else 2
    dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
    shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
    centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]

    output('dimensions:', dims)
    output('shape:     ', shape)
    output('centre:    ', centre)

    mesh0 = gen_block_mesh(dims, shape, centre, name='block-fem',
                           verbose=True)
    domain0 = FEDomain('d', mesh0)

    bbox = domain0.get_mesh_bounding_box()
    min_x, max_x = bbox[:, 0]
    eps = 1e-8 * (max_x - min_x)

    cnt = (shape[0] - 1) // 2
    g0 = 0.5 * dims[0]
    grading = nm.array([g0 / 2**ii for ii in range(cnt)]) + eps + centre[0] - g0

    domain, subs = refine_towards_facet(domain0, grading, 'x <')

    omega = domain.create_region('Omega', 'all')

    gamma1 = domain.create_region('Gamma1',
                                  'vertices in (x < %.10f)' % (min_x + eps),
                                  'facet')
    gamma2 = domain.create_region('Gamma2',
                                  'vertices in (x > %.10f)' % (max_x - eps),
                                  'facet')

    field = Field.from_args('fu', nm.float64, 1, omega,
                            approx_order=options.order)

    if subs is not None:
        field.substitute_dofs(subs)

    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    integral = Integral('i', order=2*options.order)

    t1 = Term.new('dw_laplace(v, u)',
                  integral, omega, v=v, u=u)
    eq = Equation('eq', t1)
    eqs = Equations([eq])

    def u_fun(ts, coors, bc=None, problem=None):
        """
        Define a displacement depending on the y coordinate.
        """
        if coors.shape[1] == 2:
            min_y, max_y = bbox[:, 1]
            y = (coors[:, 1] - min_y) / (max_y - min_y)

            val = (max_y - min_y) * nm.cos(3 * nm.pi * y)

        else:
            min_y, max_y = bbox[:, 1]
            min_z, max_z = bbox[:, 2]
            y = (coors[:, 1] - min_y) / (max_y - min_y)
            z = (coors[:, 2] - min_z) / (max_z - min_z)

            val = ((max_y - min_y) * (max_z - min_z)
                   * nm.cos(3 * nm.pi * y) * (1.0 + 3.0 * (z - 0.5)**2))

        return val

    bc_fun = Function('u_fun', u_fun)
    fix1 = EssentialBC('shift_u', gamma1, {'u.0' : bc_fun})
    fix2 = EssentialBC('fix2', gamma2, {'u.all' : 0.0})

    ls = ScipyDirect({})

    nls = Newton({}, lin_solver=ls)

    pb = Problem('heat', equations=eqs, nls=nls, ls=ls)

    pb.time_update(ebcs=Conditions([fix1, fix2]))
    state = pb.solve()

    if subs is not None:
        field.restore_dofs()

    filename = os.path.join(options.output_dir, 'hanging.vtk')
    ensure_path(filename)

    pb.save_state(filename, state)
    if options.order > 1:
        pb.save_state(filename, state, linearization=Struct(kind='adaptive',
                                                            min_level=0,
                                                            max_level=8,
                                                            eps=1e-3))
def main():
    parser = ArgumentParser(description=__doc__)
    parser.add_argument('--version', action='version', version='%(prog)s')
    parser.add_argument('-b',
                        '--basis',
                        metavar='name',
                        action='store',
                        dest='basis',
                        default='lagrange',
                        help=help['basis'])
    parser.add_argument('-n',
                        '--max-order',
                        metavar='order',
                        type=int,
                        action='store',
                        dest='max_order',
                        default=10,
                        help=help['max_order'])
    parser.add_argument('-m',
                        '--matrix',
                        metavar='type',
                        action='store',
                        dest='matrix_type',
                        default='laplace',
                        help=help['matrix_type'])
    parser.add_argument('-g',
                        '--geometry',
                        metavar='name',
                        action='store',
                        dest='geometry',
                        default='2_4',
                        help=help['geometry'])
    options = parser.parse_args()

    dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
    output('reference element geometry:')
    output('  dimension: %d, vertices: %d' % (dim, n_ep))

    n_c = {'laplace': 1, 'elasticity': dim}[options.matrix_type]

    output('matrix type:', options.matrix_type)
    output('number of variable components:', n_c)

    output('polynomial space:', options.basis)

    output('max. order:', options.max_order)

    mesh = Mesh.from_file(data_dir +
                          '/meshes/elements/%s_1.mesh' % options.geometry)
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')

    orders = nm.arange(1, options.max_order + 1, dtype=nm.int)
    conds = []

    order_fix = 0 if options.geometry in ['2_4', '3_8'] else 1

    for order in orders:
        output('order:', order, '...')

        field = Field.from_args('fu',
                                nm.float64,
                                n_c,
                                omega,
                                approx_order=order,
                                space='H1',
                                poly_space_base=options.basis)

        to = field.approx_order
        quad_order = 2 * (max(to - order_fix, 0))
        output('quadrature order:', quad_order)

        integral = Integral('i', order=quad_order)
        qp, _ = integral.get_qp(options.geometry)
        output('number of quadrature points:', qp.shape[0])

        u = FieldVariable('u', 'unknown', field)
        v = FieldVariable('v', 'test', field, primary_var_name='u')

        m = Material('m', D=stiffness_from_lame(dim, 1.0, 1.0), mu=1.0)

        if options.matrix_type == 'laplace':
            term = Term.new('dw_laplace(m.mu, v, u)',
                            integral,
                            omega,
                            m=m,
                            v=v,
                            u=u)
            n_zero = 1

        else:
            assert_(options.matrix_type == 'elasticity')
            term = Term.new('dw_lin_elastic(m.D, v, u)',
                            integral,
                            omega,
                            m=m,
                            v=v,
                            u=u)
            n_zero = (dim + 1) * dim / 2

        term.setup()

        output('assembling...')
        tt = time.clock()
        mtx, iels = term.evaluate(mode='weak', diff_var='u')
        output('...done in %.2f s' % (time.clock() - tt))
        mtx = mtx[0, 0]

        try:
            assert_(nm.max(nm.abs(mtx - mtx.T)) < 1e-10)

        except:
            from sfepy.base.base import debug
            debug()

        output('matrix shape:', mtx.shape)

        eigs = eig(mtx, method='eig.sgscipy', eigenvectors=False)
        eigs.sort()

        # Zero 'true' zeros.
        eigs[:n_zero] = 0.0

        ii = nm.where(eigs < 0.0)[0]
        if len(ii):
            output('matrix is not positive semi-definite!')

        ii = nm.where(eigs[n_zero:] < 1e-12)[0]
        if len(ii):
            output('matrix has more than %d zero eigenvalues!' % n_zero)

        output('smallest eigs:\n', eigs[:10])

        ii = nm.where(eigs > 0.0)[0]
        emin, emax = eigs[ii[[0, -1]]]

        output('min:', emin, 'max:', emax)

        cond = emax / emin
        conds.append(cond)

        output('condition number:', cond)

        output('...done')

    plt.figure(1)
    plt.semilogy(orders, conds)
    plt.xticks(orders, orders)
    plt.xlabel('polynomial order')
    plt.ylabel('condition number')
    plt.grid()

    plt.figure(2)
    plt.loglog(orders, conds)
    plt.xticks(orders, orders)
    plt.xlabel('polynomial order')
    plt.ylabel('condition number')
    plt.grid()

    plt.show()
Exemple #49
0
def solve_problem(mesh_filename, options, comm):
    order = options.order

    rank, size = comm.Get_rank(), comm.Get_size()

    output('rank', rank, 'of', size)

    mesh = Mesh.from_file(mesh_filename)

    if rank == 0:
        cell_tasks = pl.partition_mesh(mesh, size, use_metis=options.metis,
                                       verbose=True)

    else:
        cell_tasks = None

    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)

    output('distributing field %s...' % field.name)
    tt = time.clock()

    distribute = pl.distribute_fields_dofs
    lfds, gfds = distribute([field], cell_tasks,
                            is_overlap=True,
                            save_inter_regions=options.save_inter_regions,
                            output_dir=options.output_dir,
                            comm=comm, verbose=True)
    lfd = lfds[0]

    output('...done in', time.clock() - tt)

    if rank == 0:
        dof_maps = gfds[0].dof_maps
        id_map = gfds[0].id_map

        if options.verify:
            verify_save_dof_maps(field, cell_tasks,
                                 dof_maps, id_map, options, verbose=True)

        if options.plot:
            ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
                                  options.output_dir, size)

    output('creating local problem...')
    tt = time.clock()

    omega_gi = Region.from_cells(lfd.cells, field.domain)
    omega_gi.finalize()
    omega_gi.update_shape()

    pb = create_local_problem(omega_gi, order)

    output('...done in', time.clock() - tt)

    variables = pb.get_variables()
    eqs = pb.equations

    u_i = variables['u_i']
    field_i = u_i.field

    if options.plot:
        ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
                            options.output_dir, rank)

    output('allocating global system...')
    tt = time.clock()

    sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
    output('sizes:', sizes)
    output('drange:', drange)

    pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)

    output('pdofs:', pdofs)

    pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a, sizes, pdofs, drange,
                                              is_overlap=True, comm=comm,
                                              verbose=True)

    output('...done in', time.clock() - tt)

    output('evaluating local problem...')
    tt = time.clock()

    state = State(variables)
    state.fill(0.0)
    state.apply_ebc()

    rhs_i = eqs.eval_residuals(state())
    # This must be after pl.create_petsc_system() call!
    mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)

    output('...done in', time.clock() - tt)

    output('assembling global system...')
    tt = time.clock()

    pl.apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
    pl.assemble_rhs_to_petsc(prhs, rhs_i, pdofs, drange, is_overlap=True,
                             comm=comm, verbose=True)
    pl.assemble_mtx_to_petsc(pmtx, mtx_i, pdofs, drange, is_overlap=True,
                             comm=comm, verbose=True)

    output('...done in', time.clock() - tt)

    output('creating solver...')
    tt = time.clock()

    conf = Struct(method='cg', precond='gamg', sub_precond=None,
                  i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
    status = {}
    ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)

    output('...done in', time.clock() - tt)

    output('solving...')
    tt = time.clock()

    psol = ls(prhs, psol, conf)

    psol_i = pl.create_local_petsc_vector(pdofs)
    gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)

    scatter(psol_i, psol)

    sol0_i = state() - psol_i[...]
    psol_i[...] = sol0_i

    gather(psol, psol_i)

    output('...done in', time.clock() - tt)

    output('saving solution...')
    tt = time.clock()

    u_i.set_data(sol0_i)
    out = u_i.create_output()

    filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
    pb.domain.mesh.write(filename, io='auto', out=out)

    gather_to_zero = pl.create_gather_to_zero(psol)

    psol_full = gather_to_zero(psol)

    if comm.rank == 0:
        sol = psol_full[...].copy()[id_map]

        u = FieldVariable('u', 'parameter', field,
                          primary_var_name='(set-to-None)')

        filename = os.path.join(options.output_dir, 'sol.h5')
        if (order == 1) or (options.linearization == 'strip'):
            out = u.create_output(sol)
            mesh.write(filename, io='auto', out=out)

        else:
            out = u.create_output(sol, linearization=Struct(kind='adaptive',
                                                            min_level=0,
                                                            max_level=order,
                                                            eps=1e-3))

            out['u'].mesh.write(filename, io='auto', out=out)

    output('...done in', time.clock() - tt)

    if options.show:
        plt.show()
Exemple #50
0
def create_local_problem(omega_gi, order):
    """
    Local problem definition using a domain corresponding to the global region
    `omega_gi`.
    """
    mesh = omega_gi.domain.mesh

    # All tasks have the whole mesh.
    bbox = mesh.get_bounding_box()
    min_x, max_x = bbox[:, 0]
    eps_x = 1e-8 * (max_x - min_x)

    mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
    domain_i = FEDomain('domain_i', mesh_i)
    omega_i = domain_i.create_region('Omega', 'all')

    gamma1_i = domain_i.create_region('Gamma1',
                                      'vertices in (x < %.10f)'
                                      % (min_x + eps_x),
                                      'facet', allow_empty=True)
    gamma2_i = domain_i.create_region('Gamma2',
                                      'vertices in (x > %.10f)'
                                      % (max_x - eps_x),
                                      'facet', allow_empty=True)

    field_i = Field.from_args('fu', nm.float64, 1, omega_i,
                              approx_order=order)

    output('number of local field DOFs:', field_i.n_nod)

    u_i = FieldVariable('u_i', 'unknown', field_i)
    v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')

    integral = Integral('i', order=2*order)

    mat = Material('m', lam=10, mu=5)
    t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
                  integral, omega_i, m=mat, v_i=v_i, u_i=u_i)

    def _get_load(coors):
        val = nm.ones_like(coors[:, 0])
        for coor in coors.T:
            val *= nm.sin(4 * nm.pi * coor)
        return val

    def get_load(ts, coors, mode=None, **kwargs):
        if mode == 'qp':
            return {'val' : _get_load(coors).reshape(coors.shape[0], 1, 1)}

    load = Material('load', function=Function('get_load', get_load))

    t2 = Term.new('dw_volume_lvf(load.val, v_i)',
                  integral, omega_i, load=load, v_i=v_i)

    eq = Equation('balance', t1 - 100 * t2)
    eqs = Equations([eq])

    ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
    ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all' : 0.1})

    pb = Problem('problem_i', equations=eqs, active_only=False)
    pb.time_update(ebcs=Conditions([ebc1, ebc2]))
    pb.update_materials()

    return pb
Exemple #51
0
def main():
    parser = ArgumentParser(description=__doc__,
                            formatter_class=RawDescriptionHelpFormatter)
    parser.add_argument('--version', action='version', version='%(prog)s')
    parser.add_argument('-d', '--dims', metavar='dims',
                        action='store', dest='dims',
                        default='[1.0, 1.0]', help=helps['dims'])
    parser.add_argument('-c', '--centre', metavar='centre',
                        action='store', dest='centre',
                        default='[0.0, 0.0]', help=helps['centre'])
    parser.add_argument('-s', '--shape', metavar='shape',
                        action='store', dest='shape',
                        default='[11, 11]', help=helps['shape'])
    parser.add_argument('-b', '--bc-kind', metavar='kind',
                        action='store', dest='bc_kind',
                        choices=['free', 'cantilever', 'fixed'],
                        default='free', help=helps['bc_kind'])
    parser.add_argument('-a', '--axis', metavar='0, ..., dim, or -1',
                        type=int, action='store', dest='axis',
                        default=-1, help=helps['axis'])
    parser.add_argument('--young', metavar='float', type=float,
                        action='store', dest='young',
                        default=6.80e+10, help=helps['young'])
    parser.add_argument('--poisson', metavar='float', type=float,
                        action='store', dest='poisson',
                        default=0.36, help=helps['poisson'])
    parser.add_argument('--density', metavar='float', type=float,
                        action='store', dest='density',
                        default=2700.0, help=helps['density'])
    parser.add_argument('--order', metavar='int', type=int,
                        action='store', dest='order',
                        default=1, help=helps['order'])
    parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
                        action='store', dest='n_eigs',
                        default=6, help=helps['n_eigs'])
    parser.add_argument('-i', '--ignore', metavar='int', type=int,
                        action='store', dest='ignore',
                        default=None, help=helps['ignore'])
    parser.add_argument('--solver', metavar='solver', action='store',
                        dest='solver',
                        default= \
                        "eig.scipy,method:'eigh',tol:1e-5,maxiter:1000",
                        help=helps['solver'])
    parser.add_argument('--show',
                        action="store_true", dest='show',
                        default=False, help=helps['show'])
    parser.add_argument('filename', nargs='?', default=None)
    options = parser.parse_args()

    aux = options.solver.split(',')
    kwargs = {}
    for option in aux[1:]:
        key, val = option.split(':')
        kwargs[key.strip()] = eval(val)
    eig_conf = Struct(name='evp', kind=aux[0], **kwargs)

    output('using values:')
    output("  Young's modulus:", options.young)
    output("  Poisson's ratio:", options.poisson)
    output('  density:', options.density)
    output('displacement field approximation order:', options.order)
    output('requested %d eigenvalues' % options.n_eigs)
    output('using eigenvalue problem solver:', eig_conf.kind)
    output.level += 1
    for key, val in six.iteritems(kwargs):
        output('%s: %r' % (key, val))
    output.level -= 1

    assert_((0.0 < options.poisson < 0.5),
            "Poisson's ratio must be in ]0, 0.5[!")
    assert_((0 < options.order),
            'displacement approximation order must be at least 1!')

    filename = options.filename
    if filename is not None:
        mesh = Mesh.from_file(filename)
        dim = mesh.dim
        dims = nm.diff(mesh.get_bounding_box(), axis=0)

    else:
        dims = nm.array(eval(options.dims), dtype=nm.float64)
        dim = len(dims)

        centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
        shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]

        output('dimensions:', dims)
        output('centre:    ', centre)
        output('shape:     ', shape)

        mesh = gen_block_mesh(dims, shape, centre, name='mesh')

    output('axis:      ', options.axis)
    assert_((-dim <= options.axis < dim), 'invalid axis value!')

    eig_solver = Solver.any_from_conf(eig_conf)

    # Build the problem definition.
    domain = FEDomain('domain', mesh)

    bbox = domain.get_mesh_bounding_box()
    min_coor, max_coor = bbox[:, options.axis]
    eps = 1e-8 * (max_coor - min_coor)
    ax = 'xyz'[:dim][options.axis]

    omega = domain.create_region('Omega', 'all')
    bottom = domain.create_region('Bottom',
                                  'vertices in (%s < %.10f)'
                                  % (ax, min_coor + eps),
                                  'facet')
    bottom_top = domain.create_region('BottomTop',
                                      'r.Bottom +v vertices in (%s > %.10f)'
                                      % (ax, max_coor - eps),
                                      'facet')

    field = Field.from_args('fu', nm.float64, 'vector', omega,
                            approx_order=options.order)

    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    mtx_d = stiffness_from_youngpoisson(dim, options.young, options.poisson)

    m = Material('m', D=mtx_d, rho=options.density)

    integral = Integral('i', order=2*options.order)

    t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
    t2 = Term.new('dw_volume_dot(m.rho, v, u)', integral, omega, m=m, v=v, u=u)
    eq1 = Equation('stiffness', t1)
    eq2 = Equation('mass', t2)
    lhs_eqs = Equations([eq1, eq2])

    pb = Problem('modal', equations=lhs_eqs)

    if options.bc_kind == 'free':
        pb.time_update()
        n_rbm = dim * (dim + 1) / 2

    elif options.bc_kind == 'cantilever':
        fixed = EssentialBC('Fixed', bottom, {'u.all' : 0.0})
        pb.time_update(ebcs=Conditions([fixed]))
        n_rbm = 0

    elif options.bc_kind == 'fixed':
        fixed = EssentialBC('Fixed', bottom_top, {'u.all' : 0.0})
        pb.time_update(ebcs=Conditions([fixed]))
        n_rbm = 0

    else:
        raise ValueError('unsupported BC kind! (%s)' % options.bc_kind)

    if options.ignore is not None:
        n_rbm = options.ignore

    pb.update_materials()

    # Assemble stiffness and mass matrices.
    mtx_k = eq1.evaluate(mode='weak', dw_mode='matrix', asm_obj=pb.mtx_a)
    mtx_m = mtx_k.copy()
    mtx_m.data[:] = 0.0
    mtx_m = eq2.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx_m)

    try:
        eigs, svecs = eig_solver(mtx_k, mtx_m, options.n_eigs + n_rbm,
                                 eigenvectors=True)

    except sla.ArpackNoConvergence as ee:
        eigs = ee.eigenvalues
        svecs = ee.eigenvectors
        output('only %d eigenvalues converged!' % len(eigs))

    output('%d eigenvalues converged (%d ignored as rigid body modes)' %
           (len(eigs), n_rbm))

    eigs = eigs[n_rbm:]
    svecs = svecs[:, n_rbm:]

    omegas = nm.sqrt(eigs)
    freqs = omegas / (2 * nm.pi)

    output('number |         eigenvalue |  angular frequency '
           '|          frequency')
    for ii, eig in enumerate(eigs):
        output('%6d | %17.12e | %17.12e | %17.12e'
               % (ii + 1, eig, omegas[ii], freqs[ii]))

    # Make full eigenvectors (add DOFs fixed by boundary conditions).
    variables = pb.get_variables()

    vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
                    dtype=nm.float64)
    for ii in range(svecs.shape[1]):
        vecs[:, ii] = variables.make_full_vec(svecs[:, ii])

    # Save the eigenvectors.
    out = {}
    state = pb.create_state()
    for ii in range(eigs.shape[0]):
        state.set_full(vecs[:, ii])
        aux = state.create_output_dict()
        strain = pb.evaluate('ev_cauchy_strain.i.Omega(u)',
                             integrals=Integrals([integral]),
                             mode='el_avg', verbose=False)
        out['u%03d' % ii] = aux.popitem()[1]
        out['strain%03d' % ii] = Struct(mode='cell', data=strain)

    pb.save_state('eigenshapes.vtk', out=out)
    pb.save_regions_as_groups('regions')

    if len(eigs) and options.show:
        # Show the solution. If the approximation order is greater than 1, the
        # extra DOFs are simply thrown away.
        from sfepy.postprocess.viewer import Viewer
        from sfepy.postprocess.domain_specific import DomainSpecificPlot

        scaling = 0.05 * dims.max() / nm.abs(vecs).max()

        ds = {}
        for ii in range(eigs.shape[0]):
            pd = DomainSpecificPlot('plot_displacements',
                                    ['rel_scaling=%s' % scaling,
                                     'color_kind="tensors"',
                                     'color_name="strain%03d"' % ii])
            ds['u%03d' % ii] = pd

        view = Viewer('eigenshapes.vtk')
        view(domain_specific=ds, only_names=sorted(ds.keys()),
             is_scalar_bar=False, is_wireframe=True)
def solve_problem(mesh_filename, options, comm):
    order = options.order

    rank, size = comm.Get_rank(), comm.Get_size()

    output('rank', rank, 'of', size)

    mesh = Mesh.from_file(mesh_filename)

    if rank == 0:
        cell_tasks = pl.partition_mesh(mesh,
                                       size,
                                       use_metis=options.metis,
                                       verbose=True)

    else:
        cell_tasks = None

    output('creating global domain and field...')
    tt = time.clock()
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
    output('...done in', time.clock() - tt)

    output('distributing field %s...' % field.name)
    tt = time.clock()

    distribute = pl.distribute_fields_dofs
    lfds, gfds = distribute([field],
                            cell_tasks,
                            is_overlap=True,
                            save_inter_regions=options.save_inter_regions,
                            output_dir=options.output_dir,
                            comm=comm,
                            verbose=True)
    lfd = lfds[0]

    output('...done in', time.clock() - tt)

    if rank == 0:
        dof_maps = gfds[0].dof_maps
        id_map = gfds[0].id_map

        if options.verify:
            verify_save_dof_maps(field,
                                 cell_tasks,
                                 dof_maps,
                                 id_map,
                                 options,
                                 verbose=True)

        if options.plot:
            ppd.plot_partitioning([None, None], field, cell_tasks, gfds[0],
                                  options.output_dir, size)

    output('creating local problem...')
    tt = time.clock()

    omega_gi = Region.from_cells(lfd.cells, field.domain)
    omega_gi.finalize()
    omega_gi.update_shape()

    pb = create_local_problem(omega_gi, order)

    output('...done in', time.clock() - tt)

    variables = pb.get_variables()
    eqs = pb.equations

    u_i = variables['u_i']
    field_i = u_i.field

    if options.plot:
        ppd.plot_local_dofs([None, None], field, field_i, omega_gi,
                            options.output_dir, rank)

    output('allocating global system...')
    tt = time.clock()

    sizes, drange = pl.get_sizes(lfd.petsc_dofs_range, field.n_nod, 1)
    output('sizes:', sizes)
    output('drange:', drange)

    pdofs = pl.get_local_ordering(field_i, lfd.petsc_dofs_conn)

    output('pdofs:', pdofs)

    pmtx, psol, prhs = pl.create_petsc_system(pb.mtx_a,
                                              sizes,
                                              pdofs,
                                              drange,
                                              is_overlap=True,
                                              comm=comm,
                                              verbose=True)

    output('...done in', time.clock() - tt)

    output('evaluating local problem...')
    tt = time.clock()

    state = State(variables)
    state.fill(0.0)
    state.apply_ebc()

    rhs_i = eqs.eval_residuals(state())
    # This must be after pl.create_petsc_system() call!
    mtx_i = eqs.eval_tangent_matrices(state(), pb.mtx_a)

    output('...done in', time.clock() - tt)

    output('assembling global system...')
    tt = time.clock()

    apply_ebc_to_matrix(mtx_i, u_i.eq_map.eq_ebc)
    pl.assemble_rhs_to_petsc(prhs,
                             rhs_i,
                             pdofs,
                             drange,
                             is_overlap=True,
                             comm=comm,
                             verbose=True)
    pl.assemble_mtx_to_petsc(pmtx,
                             mtx_i,
                             pdofs,
                             drange,
                             is_overlap=True,
                             comm=comm,
                             verbose=True)

    output('...done in', time.clock() - tt)

    output('creating solver...')
    tt = time.clock()

    conf = Struct(method='cg',
                  precond='gamg',
                  sub_precond='none',
                  i_max=10000,
                  eps_a=1e-50,
                  eps_r=1e-5,
                  eps_d=1e4,
                  verbose=True)
    status = {}
    ls = PETScKrylovSolver(conf, comm=comm, mtx=pmtx, status=status)

    output('...done in', time.clock() - tt)

    output('solving...')
    tt = time.clock()

    psol = ls(prhs, psol)

    psol_i = pl.create_local_petsc_vector(pdofs)
    gather, scatter = pl.create_gather_scatter(pdofs, psol_i, psol, comm=comm)

    scatter(psol_i, psol)

    sol0_i = state() - psol_i[...]
    psol_i[...] = sol0_i

    gather(psol, psol_i)

    output('...done in', time.clock() - tt)

    output('saving solution...')
    tt = time.clock()

    u_i.set_data(sol0_i)
    out = u_i.create_output()

    filename = os.path.join(options.output_dir, 'sol_%02d.h5' % comm.rank)
    pb.domain.mesh.write(filename, io='auto', out=out)

    gather_to_zero = pl.create_gather_to_zero(psol)

    psol_full = gather_to_zero(psol)

    if comm.rank == 0:
        sol = psol_full[...].copy()[id_map]

        u = FieldVariable('u',
                          'parameter',
                          field,
                          primary_var_name='(set-to-None)')

        filename = os.path.join(options.output_dir, 'sol.h5')
        if (order == 1) or (options.linearization == 'strip'):
            out = u.create_output(sol)
            mesh.write(filename, io='auto', out=out)

        else:
            out = u.create_output(sol,
                                  linearization=Struct(kind='adaptive',
                                                       min_level=0,
                                                       max_level=order,
                                                       eps=1e-3))

            out['u'].mesh.write(filename, io='auto', out=out)

    output('...done in', time.clock() - tt)

    if options.show:
        plt.show()
def main():
    parser = OptionParser(usage=usage, version='%prog')
    parser.add_option('-b', '--basis', metavar='name',
                      action='store', dest='basis',
                      default='lagrange', help=help['basis'])
    parser.add_option('-n', '--max-order', metavar='order', type=int,
                      action='store', dest='max_order',
                      default=10, help=help['max_order'])
    parser.add_option('-m', '--matrix', metavar='type',
                      action='store', dest='matrix_type',
                      default='laplace', help=help['matrix_type'])
    parser.add_option('-g', '--geometry', metavar='name',
                      action='store', dest='geometry',
                      default='2_4', help=help['geometry'])
    options, args = parser.parse_args()

    dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
    output('reference element geometry:')
    output('  dimension: %d, vertices: %d' % (dim, n_ep))

    n_c = {'laplace' : 1, 'elasticity' : dim}[options.matrix_type]

    output('matrix type:', options.matrix_type)
    output('number of variable components:',  n_c)

    output('polynomial space:', options.basis)

    output('max. order:', options.max_order)

    mesh = Mesh.from_file(data_dir + '/meshes/elements/%s_1.mesh'
                          % options.geometry)
    domain = FEDomain('domain', mesh)
    omega = domain.create_region('Omega', 'all')

    orders = nm.arange(1, options.max_order + 1, dtype=nm.int)
    conds = []

    order_fix = 0 if  options.geometry in ['2_4', '3_8'] else 1

    for order in orders:
        output('order:', order, '...')

        field = Field.from_args('fu', nm.float64, n_c, omega,
                                approx_order=order,
                                space='H1', poly_space_base=options.basis)

        to = field.approx_order
        quad_order = 2 * (max(to - order_fix, 0))
        output('quadrature order:', quad_order)

        integral = Integral('i', order=quad_order)
        qp, _ = integral.get_qp(options.geometry)
        output('number of quadrature points:', qp.shape[0])

        u = FieldVariable('u', 'unknown', field)
        v = FieldVariable('v', 'test', field, primary_var_name='u')

        m = Material('m', lam=1.0, mu=1.0)

        if options.matrix_type == 'laplace':
            term = Term.new('dw_laplace(m.mu, v, u)',
                            integral, omega, m=m, v=v, u=u)
            n_zero = 1

        else:
            assert_(options.matrix_type == 'elasticity')
            term = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
                            integral, omega, m=m, v=v, u=u)
            n_zero = (dim + 1) * dim / 2

        term.setup()

        output('assembling...')
        tt = time.clock()
        mtx, iels = term.evaluate(mode='weak', diff_var='u')
        output('...done in %.2f s' % (time.clock() - tt))
        mtx = mtx[0][0, 0]

        try:
            assert_(nm.max(nm.abs(mtx - mtx.T)) < 1e-10)

        except:
            from sfepy.base.base import debug; debug()

        output('matrix shape:', mtx.shape)

        eigs = eig(mtx, method='eig.sgscipy', eigenvectors=False)
        eigs.sort()

        # Zero 'true' zeros.
        eigs[:n_zero] = 0.0

        ii = nm.where(eigs < 0.0)[0]
        if len(ii):
            output('matrix is not positive semi-definite!')

        ii = nm.where(eigs[n_zero:] < 1e-12)[0]
        if len(ii):
            output('matrix has more than %d zero eigenvalues!' % n_zero)

        output('smallest eigs:\n', eigs[:10])

        ii = nm.where(eigs > 0.0)[0]
        emin, emax = eigs[ii[[0, -1]]]

        output('min:', emin, 'max:', emax)

        cond = emax / emin
        conds.append(cond)

        output('condition number:', cond)

        output('...done')

    plt.figure(1)
    plt.semilogy(orders, conds)
    plt.xticks(orders, orders)
    plt.xlabel('polynomial order')
    plt.ylabel('condition number')
    plt.grid()

    plt.figure(2)
    plt.loglog(orders, conds)
    plt.xticks(orders, orders)
    plt.xlabel('polynomial order')
    plt.ylabel('condition number')
    plt.grid()

    plt.show()
Exemple #54
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def main():
    from sfepy import data_dir

    parser = OptionParser(usage=usage, version='%prog')
    parser.add_option('-s',
                      '--show',
                      action="store_true",
                      dest='show',
                      default=False,
                      help=help['show'])
    options, args = parser.parse_args()

    mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
    domain = FEDomain('domain', mesh)

    min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
    eps = 1e-8 * (max_x - min_x)
    omega = domain.create_region('Omega', 'all')
    gamma1 = domain.create_region('Gamma1',
                                  'vertices in x < %.10f' % (min_x + eps),
                                  'facet')
    gamma2 = domain.create_region('Gamma2',
                                  'vertices in x > %.10f' % (max_x - eps),
                                  'facet')

    field = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)

    u = FieldVariable('u', 'unknown', field)
    v = FieldVariable('v', 'test', field, primary_var_name='u')

    m = Material('m', D=stiffness_from_lame(dim=2, lam=1.0, mu=1.0))
    f = Material('f', val=[[0.02], [0.01]])

    integral = Integral('i', order=3)

    t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
    t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
    eq = Equation('balance', t1 + t2)
    eqs = Equations([eq])

    fix_u = EssentialBC('fix_u', gamma1, {'u.all': 0.0})

    bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift': 0.01})
    shift_u = EssentialBC('shift_u', gamma2, {'u.0': bc_fun})

    ls = ScipyDirect({})

    nls_status = IndexedStruct()
    nls = Newton({}, lin_solver=ls, status=nls_status)

    pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
    pb.save_regions_as_groups('regions')

    pb.time_update(ebcs=Conditions([fix_u, shift_u]))

    vec = pb.solve()
    print(nls_status)

    pb.save_state('linear_elasticity.vtk', vec)

    if options.show:
        view = Viewer('linear_elasticity.vtk')
        view(vector_mode='warp_norm',
             rel_scaling=2,
             is_scalar_bar=True,
             is_wireframe=True)
def save_basis_on_mesh(mesh, options, output_dir, lin,
                       permutations=None, suffix=''):
    if permutations is not None:
        mesh = mesh.copy()
        gel = GeometryElement(mesh.descs[0])
        perms = gel.get_conn_permutations()[permutations]
        conn = mesh.cmesh.get_cell_conn()
        n_el, n_ep = conn.num, gel.n_vertex
        offsets = nm.arange(n_el) * n_ep

        conn.indices[:] = conn.indices.take((perms + offsets[:, None]).ravel())

    domain = FEDomain('domain', mesh)

    omega = domain.create_region('Omega', 'all')
    field = Field.from_args('f', nm.float64, shape=1, region=omega,
                            approx_order=options.max_order,
                            poly_space_base=options.basis)
    var = FieldVariable('u', 'unknown', field)

    if options.plot_dofs:
        import sfepy.postprocess.plot_dofs as pd
        import sfepy.postprocess.plot_cmesh as pc
        ax = pc.plot_wireframe(None, mesh.cmesh)
        ax = pd.plot_global_dofs(ax, field.get_coor(), field.econn)
        ax = pd.plot_local_dofs(ax, field.get_coor(), field.econn)
        if options.dofs is not None:
            ax = pd.plot_nodes(ax, field.get_coor(), field.econn,
                               field.poly_space.nodes,
                               get_dofs(options.dofs, var.n_dof))
        pd.plt.show()

    output('dofs: %d' % var.n_dof)

    vec = nm.empty(var.n_dof, dtype=var.dtype)
    n_digit, _format = get_print_info(var.n_dof, fill='0')
    name_template = os.path.join(output_dir,
                                 'dof_%s%s.vtk' % (_format, suffix))
    for ip in get_dofs(options.dofs, var.n_dof):
        output('dof %d...' % ip)

        vec.fill(0.0)
        vec[ip] = 1.0

        var.set_data(vec)

        if options.derivative == 0:
            out = var.create_output(vec, linearization=lin)

        else:
            out = create_expression_output('ev_grad.ie.Elements(u)',
                                           'u', 'f', {'f' : field}, None,
                                           Variables([var]),
                                           mode='qp', verbose=False,
                                           min_level=lin.min_level,
                                           max_level=lin.max_level,
                                           eps=lin.eps)

        name = name_template % ip
        ensure_path(name)
        out['u'].mesh.write(name, out=out)

        output('...done (%s)' % name)
Exemple #56
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def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
                   material_value=None, poly_space_base=None):
    from sfepy.base.base import basestr
    from sfepy.discrete import FieldVariable, Material, Variables, Materials
    from sfepy.discrete.fem import Field
    from sfepy.solvers.ts import TimeStepper
    from sfepy.mechanics.tensors import dim2sym

    omega = domain.regions['Omega']
    dim = domain.shape.dim
    sym = dim2sym(dim)

    def _parse_scalar_shape(sh):
        if isinstance(sh, basestr):
            if sh == 'D':
                return dim

            elif sh == 'D2':
                return dim**2

            elif sh == 'S':
                return sym

            elif sh == 'N': # General number ;)
                return 1

            else:
                return int(sh)

        else:
            return sh

    def _parse_tuple_shape(sh):
        if isinstance(sh, basestr):
            return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]

        else:
            return (int(sh),)

    args = {}
    str_args = []
    materials = []
    variables = []
    for ii, arg_kind in enumerate(arg_kinds):
        if arg_kind != 'ts':
            if ats_mode is not None:
                extended_ats = arg_types[ii] + ('/%s' % ats_mode)

            else:
                extended_ats = arg_types[ii]

            try:
                sh = arg_shapes[arg_types[ii]]

            except KeyError:
                sh = arg_shapes[extended_ats]

        if arg_kind.endswith('variable'):
            shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
            field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
                                    approx_order=1,
                                    poly_space_base=poly_space_base)

            if arg_kind == 'virtual_variable':
                if sh[1] is not None:
                    istate = arg_types.index(sh[1])

                else:
                    # Only virtual variable in arguments.
                    istate = -1
                    # -> Make fake variable.
                    var = FieldVariable('u-1', 'unknown', field)
                    var.set_constant(0.0)
                    variables.append(var)

                var = FieldVariable('v', 'test', field,
                                    primary_var_name='u%d' % istate)

            elif arg_kind == 'state_variable':
                var = FieldVariable('u%d' % ii, 'unknown', field)
                var.set_constant(0.0)

            elif arg_kind == 'parameter_variable':
                var = FieldVariable('p%d' % ii, 'parameter', field,
                                    primary_var_name='(set-to-None)')
                var.set_constant(0.0)

            variables.append(var)
            str_args.append(var.name)
            args[var.name] = var

        elif arg_kind.endswith('material'):
            if sh is None: # Switched-off opt_material.
                continue

            prefix = ''
            if isinstance(sh, basestr):
                aux = sh.split(':')
                if len(aux) == 2:
                    prefix, sh = aux

            if material_value is None:
                material_value = 1.0

            shape = _parse_tuple_shape(sh)
            if (len(shape) > 1) or (shape[0] > 1):
                if ((len(shape) == 2) and (shape[0] ==  shape[1])
                    and (material_value != 0.0)):
                    # Identity matrix.
                    val = nm.eye(shape[0], dtype=nm.float64)

                else:
                    # Array.
                    val = nm.empty(shape, dtype=nm.float64)
                    val.fill(material_value)

                values = {'%sc%d' % (prefix, ii)
                          : val}

            elif (len(shape) == 1) and (shape[0] == 1):
                # Single scalar as a special value.
                values = {'.c%d' % ii : material_value}

            else:
                raise ValueError('wrong material shape! (%s)' % shape)

            mat = Material('m%d' % ii, values=values)

            materials.append(mat)
            str_args.append(mat.name + '.' + 'c%d' % ii)
            args[mat.name] = mat

        elif arg_kind == 'ts':
            ts = TimeStepper(0.0, 1.0, 1.0, 5)
            str_args.append('ts')
            args['ts'] = ts

        else:
            str_args.append('user%d' % ii)
            args[str_args[-1]] = None

    materials = Materials(materials)
    variables = Variables(variables)

    return args, str_args, materials, variables
Exemple #57
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def create_local_problem(omega_gi, orders):
    """
    Local problem definition using a domain corresponding to the global region
    `omega_gi`.
    """
    order_u, order_p = orders

    mesh = omega_gi.domain.mesh

    # All tasks have the whole mesh.
    bbox = mesh.get_bounding_box()
    min_x, max_x = bbox[:, 0]
    eps_x = 1e-8 * (max_x - min_x)

    min_y, max_y = bbox[:, 1]
    eps_y = 1e-8 * (max_y - min_y)

    mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
    domain_i = FEDomain('domain_i', mesh_i)
    omega_i = domain_i.create_region('Omega', 'all')

    gamma1_i = domain_i.create_region('Gamma1',
                                      'vertices in (x < %.10f)'
                                      % (min_x + eps_x),
                                      'facet', allow_empty=True)
    gamma2_i = domain_i.create_region('Gamma2',
                                      'vertices in (x > %.10f)'
                                      % (max_x - eps_x),
                                      'facet', allow_empty=True)
    gamma3_i = domain_i.create_region('Gamma3',
                                      'vertices in (y < %.10f)'
                                      % (min_y + eps_y),
                                      'facet', allow_empty=True)

    field1_i = Field.from_args('fu', nm.float64, mesh.dim, omega_i,
                               approx_order=order_u)

    field2_i = Field.from_args('fp', nm.float64, 1, omega_i,
                               approx_order=order_p)

    output('field 1: number of local DOFs:', field1_i.n_nod)
    output('field 2: number of local DOFs:', field2_i.n_nod)

    u_i = FieldVariable('u_i', 'unknown', field1_i, order=0)
    v_i = FieldVariable('v_i', 'test', field1_i, primary_var_name='u_i')
    p_i = FieldVariable('p_i', 'unknown', field2_i, order=1)
    q_i = FieldVariable('q_i', 'test', field2_i, primary_var_name='p_i')

    if mesh.dim == 2:
        alpha = 1e2 * nm.array([[0.132], [0.132], [0.092]])

    else:
        alpha = 1e2 * nm.array([[0.132], [0.132], [0.132],
                                [0.092], [0.092], [0.092]])

    mat = Material('m', D=stiffness_from_lame(mesh.dim, lam=10, mu=5),
                   k=1, alpha=alpha)
    integral = Integral('i', order=2*(max(order_u, order_p)))

    t11 = Term.new('dw_lin_elastic(m.D, v_i, u_i)',
                   integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
    t12 = Term.new('dw_biot(m.alpha, v_i, p_i)',
                   integral, omega_i, m=mat, v_i=v_i, p_i=p_i)
    t21 = Term.new('dw_biot(m.alpha, u_i, q_i)',
                   integral, omega_i, m=mat, u_i=u_i, q_i=q_i)
    t22 = Term.new('dw_laplace(m.k, q_i, p_i)',
                   integral, omega_i, m=mat, q_i=q_i, p_i=p_i)

    eq1 = Equation('eq1', t11 - t12)
    eq2 = Equation('eq1', t21 + t22)
    eqs = Equations([eq1, eq2])

    ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
    ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.0' : 0.05})
    def bc_fun(ts, coors, **kwargs):
        val = 0.3 * nm.sin(4 * nm.pi * (coors[:, 0] - min_x) / (max_x - min_x))
        return val

    fun = Function('bc_fun', bc_fun)
    ebc3 = EssentialBC('ebc3', gamma3_i, {'p_i.all' : fun})

    pb = Problem('problem_i', equations=eqs, active_only=False)
    pb.time_update(ebcs=Conditions([ebc1, ebc2, ebc3]))
    pb.update_materials()

    return pb
def create_local_problem(omega_gi, orders):
    """
    Local problem definition using a domain corresponding to the global region
    `omega_gi`.
    """
    order_u, order_p = orders

    mesh = omega_gi.domain.mesh

    # All tasks have the whole mesh.
    bbox = mesh.get_bounding_box()
    min_x, max_x = bbox[:, 0]
    eps_x = 1e-8 * (max_x - min_x)

    min_y, max_y = bbox[:, 1]
    eps_y = 1e-8 * (max_y - min_y)

    mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
    domain_i = FEDomain('domain_i', mesh_i)
    omega_i = domain_i.create_region('Omega', 'all')

    gamma1_i = domain_i.create_region('Gamma1',
                                      'vertices in (x < %.10f)'
                                      % (min_x + eps_x),
                                      'facet', allow_empty=True)
    gamma2_i = domain_i.create_region('Gamma2',
                                      'vertices in (x > %.10f)'
                                      % (max_x - eps_x),
                                      'facet', allow_empty=True)
    gamma3_i = domain_i.create_region('Gamma3',
                                      'vertices in (y < %.10f)'
                                      % (min_y + eps_y),
                                      'facet', allow_empty=True)

    field1_i = Field.from_args('fu', nm.float64, mesh.dim, omega_i,
                               approx_order=order_u)

    field2_i = Field.from_args('fp', nm.float64, 1, omega_i,
                               approx_order=order_p)

    output('field 1: number of local DOFs:', field1_i.n_nod)
    output('field 2: number of local DOFs:', field2_i.n_nod)

    u_i = FieldVariable('u_i', 'unknown', field1_i, order=0)
    v_i = FieldVariable('v_i', 'test', field1_i, primary_var_name='u_i')
    p_i = FieldVariable('p_i', 'unknown', field2_i, order=1)
    q_i = FieldVariable('q_i', 'test', field2_i, primary_var_name='p_i')

    if mesh.dim == 2:
        alpha = 1e2 * nm.array([[0.132], [0.132], [0.092]])

    else:
        alpha = 1e2 * nm.array([[0.132], [0.132], [0.132],
                                [0.092], [0.092], [0.092]])

    mat = Material('m', D=stiffness_from_lame(mesh.dim, lam=10, mu=5),
                   k=1, alpha=alpha)
    integral = Integral('i', order=2*(max(order_u, order_p)))

    t11 = Term.new('dw_lin_elastic(m.D, v_i, u_i)',
                   integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
    t12 = Term.new('dw_biot(m.alpha, v_i, p_i)',
                   integral, omega_i, m=mat, v_i=v_i, p_i=p_i)
    t21 = Term.new('dw_biot(m.alpha, u_i, q_i)',
                   integral, omega_i, m=mat, u_i=u_i, q_i=q_i)
    t22 = Term.new('dw_laplace(m.k, q_i, p_i)',
                   integral, omega_i, m=mat, q_i=q_i, p_i=p_i)

    eq1 = Equation('eq1', t11 - t12)
    eq2 = Equation('eq1', t21 + t22)
    eqs = Equations([eq1, eq2])

    ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
    ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.0' : 0.05})
    def bc_fun(ts, coors, **kwargs):
        val = 0.3 * nm.sin(4 * nm.pi * (coors[:, 0] - min_x) / (max_x - min_x))
        return val

    fun = Function('bc_fun', bc_fun)
    ebc3 = EssentialBC('ebc3', gamma3_i, {'p_i.all' : fun})

    pb = Problem('problem_i', equations=eqs, active_only=False)
    pb.time_update(ebcs=Conditions([ebc1, ebc2, ebc3]))
    pb.update_materials()

    return pb